I had this issue repaired by Apple on my 2011 MBP and wanted to provide some advice to those considering the $310 repair. While there is no chance (at this time) to get the repair done for free (even though that would be the right thing for Apple to do), you can get Apple to do it for less than $310.
Several weeks ago, someone posted here that he got the $310 repair done for half price. So, when I went into the Apple Store, I knew that someone in that store had the power to discount the cost by 50%. I succeeded in getting my logic board replaced for $155 at the Apple Store.
The key here is to be prepared when you go to the store: leave yourself plenty of time (at least 1-2 hours), take a bottled water, and use the bathroom before arriving. If you go with a friend, make sure they understand that you will be in it for the long haul.
Here are a few important notes about talking to the "genius":
1. Before you go, set a goal and prepare yourself to stick to it. Your goal should be to get the $310 repair for half-price, which is not unreasonable. If you set an unreasonable goal, you will likely walk out empty handed. However, you need to keep this goal hidden until the very end of the discussion. When you first start talking to the genius, you need to make it appear that you are not willing to pay anything for the repair. You will eventually be negotiating to the fallback position of a 50% discount.
2. Employees at the Apple store are taught how make the customer feel good. Even when they are giving you bad news, it doesn't sting so badly. They have flexibility in what they can do for you, but they will first try to make you happy while sticking to the "by the book" solution. The trick is not to go in angry. If you go in angry, you will never get to the point of them being flexible.
You also want to keep your goal in mind and keep directing the conversation towards it. Use words that they use, like "owning the customer’s problem" or "as a customer, I will not be leaving here satisfied." Try your best to stay calm and build sympathy by using the kinds of words that they hear in training.
3. Be patient. Getting a discount will not come in the first 30 minutes of discussion. It took me 90 minutes. Keep them talking and always take advantage of opportunities to expound more. Ask to repeat the options, discuss what happens when the replaced board goes bad, and so on. You want your genius bar appointment to start bumping into other customer's appointments. Try to set your appointment in the evening when the store is busiest. Do not leave the store until you have reached your goal.
4. The first thing they will try to do is try to make you feel like you are the only one with this issue. As long as this issue isn't common, then there is no reason they should give you a break on price. I took printouts of every article that I could find on every major news website. I laid them all out in front of the genius and cluttered up the bar. Make sure that they know that you know that you are not alone.
5. The next thing they will bring up is that you should have purchased AppleCare. The point I made to them is that AppleCare is for issues like hard drives, bad keys on the keyboards, bad RAM, and screen hinges going out. It is also for anomalies that only affect a handful of people. However, it is not appropriate to say that I should buy AppleCare to cover a ticking time-bomb that is affecting thousands of users and that was built into the computer right out of the factory. Otherwise, how can I ever trust another Apple computer ever again? Since it is just now happening with the 2011s, it will be a year before we know if the 2012s are affected, two years for the 2013s, and so on. Offering an optional AppleCare warranty does not give them a pass on designing computers to fail.
6. The next thing they will do is say that they are just lowly employees and have no other options to offer you. The genius will try to make you feel bad personally for them, rather than seeing them as a face of the corporation that is in the process of screwing you. If you are a guy, I have seen them call over a female genius because it can be much harder for some guys to stay upset with a woman.
You need to ask for a manager. They will bring over a mid-level manager. That person also has no power to help you beyond the standard answers. However, eventually that is the person that will need to go to the store manager and get permission to give you a 50% discount. When the mid-level manager arrives, start at the very beginning of your story and go through it in detail (this eats up more time).
As a side note, the mid-level manager at the store I went to pretended that my issue was uncommon. However, by the end of the conversation, he let me know that he has had several customers in with this exact same issue. He told me that some of his customers actually went to a place in the area that does reballing. The manager pointed out that he knew that that was the only real solution since Apple's repair boards are exactly the same as their originals. My point here is that the geniuses and managers see support as a bit of a word game and don't always give you the right (i.e., honest) information first, even when they know it is the only way you will really get your problem solved.
7. At some point along the way, the geniuses said that the only way they could do something for me was if I called AppleCare and got it approved. I knew that they were just giving me the run around. Rather than leaving the store to call AppleCare, I called while sitting at the genius bar. Again, I started at the very beginning of the story and ate up more time for them. I asked for a supervisor for the phone support as well.
By the way, Apple's phone system will try to make you authorize paid support when calling. To get around this, mumble to the computer. If their computer phone system doesn't understand you, then it will send you to a real person. As expected, the phone support told me that all they could do is make me an appointment at the genius bar, where I was currently sitting.
8. One of the most effective arguments that I posed was that the replacement boards seem to be failing even faster than the original ones. I keep reading about people who are going through 3 and 4 replacements. At that rate, you really aren't buying a computer any longer -- instead you have been renting it for around $100 per month. How does that make any sense to anyone? Since the standard tests often do not reveal the problems on the boards, it is easy for Apple to replace your board with another broken one. Due to the intermittent nature of the issue, it could be months before it crops up again. How can the genius guarantee that the new board will work? Given the reports of failure, how can they justify only a 90 day warranty? The geniuses at my Apple Store had a very hard time answering this.
9. Ok, so by this time you should be about and hour or two into the process. It should be dawning on them that you are not going away. You are bumping into their other appointments and will start showing up on their customer service reports. This is when you need to start negotiating to a 50% discount. The point I made to them was this: "ok, yes, when I buy anything, I take a certain risk -- I get it. And even though this is a clear manufacturing and design error, I understand that Apple has given you little that they can do for me. However, I have no way of knowing that this $310 is the last $310 that I will need to spend on this computer for this issue. In fact, according to most reports, it is unlikely to permanently address my issue. Based on that, can we at least call it in the middle? I will pay for half. Then, when the board goes bad again, I will use the money I saved to go get the GPU reballed with proper lead solder."
Anyway, I cannot guarantee that this method will work for you, but it did get me the repair for $155. I found that a lot easier to stomach than $310. I hope this helps someone else save a little money.