Thank you corentiny1 for finding this and telling us!
And thank you Apple for finally recognising the problem and acting on it.
I don't know however if they will reimburse me my first logic board replacement as just after the 4th logic board replacement, in January this year while it was still working OK, I contacted Apple Support by chat, pointing out that the subject concerned a recently added Apple component in order to avoid having to pay to chat.
I expected the 4th replacement board to fail before the process with Apple finished, but no - the chat resulted very quickly in a telephone call from a Senior Adviser in Apple in Ireland, extremely helpful and pleasant, who agreed to replace my early 2011 (i7 8GB memory 500 GB disc with the dreaded AMD processor) MacBook Pro with a new 2014 (so current) 15 inch i7 Retina (16 GB 500 GB SSD) MacBook Pro. He agreed I could pay the normal upgrade price to upgrade to the 2.8 GHz i7 and a 1TB SSD, which I did. This meant they collected my machine, which I had managed to Time Machine AND Carbon Copy Clone and I duly de-registered iTunes etc. and wiped the disc. And because of the extras they delivered the new machine from China to me in Belgium, which took 6 days. This part of the operation was followed by a very helpful lady from AppleCare Support in the Netherlands (by the way I had never bothered with AppleCare as until that machine, all the Macs in my family had been extremely reliable and long-lived). One thing the Senior Adviser said was "as you have paid for the first of a series of faulty repairs", which is why I don't know if they will reimburse it, having replaced the whole machine.
Another thing - I told him I had bought the machine partly to run professional graphics and photography applications on and that this was impossible with the failed logic boards - he seemed a bit surprised and said most people seemed to buy high-end machines even though they had no real technical need of them and just used them for email, web access and bit of office applications. I pointed out the huge tip of the enormous iceberg of hurt professional users on this thread; another factor being that most of us seem to be highly mobile - for example I spend a quarter of my days travelling or away from base and thus an iMac or a Mac Pro are not much use to me.
Nonetheless I shall send in the request and see what happens. I have the serial number and characteristics of the faulty machine and all the proofs of the multiple repairs.
Now for something interesting - I had decided to do do a clean install of my software and files on the Yosemite the machine came with, rather than taking over the cumbersome layers upon layers of old stuff accumulated since Tiger, Leopard, Snow Leopard, Lion, Mountain Lion and Mavericks, and had expected to need to do this by transferring stuff gradually from the clone, as I had thought this Yosemite machine would not run Mavericks, having heard that new machines would not run previous operating systems. Nonetheless I created a second partition on this huge SSD and cloned my Mavericks clone to it, and lo and behold, it worked immediately like a charm. Presumably because the machine is technically a "mid-2014" model while Yosemite was officially launched on 16 October 2014. This means I can gradually transfer programmes and stuff as I need them, and use my Mavericks partition directly when required. I also have an old emergency Snow Leopard partition cloned, but this would indeed not boot immediately and I have not had time to investigate further, probably impossible and not worth it.
One small detail - I couldn't get the iWork '09 applications to work under Yosemite until some helpful people in another thread pointed out that one needed to load them from a .dmg or a DVD and update it, the only problem being that it's disappeared from iTunes and the AppStore so one has to update it from elsewhere (I still have the original DVD, luckily).
Once again, thanks Apple for at last recognising the problem and at least offering to repair free of charge. Even though the free-of-charge logic board will certainly need replacement several times! But personally I am extremely pleased at this outcome. Good luck everybody and thank you for our collective voice, advice, experience-sharing and support. AND as D3us said, thanks to all of you who have so tirelessly and doggedly campaigned on this issue, digging up facts and expertise, petitioning, collecting serial numbers etc.