Mid 2012 Retina MBP Battery replacement cost

Hi all, my trusty Mid-2012 15" Retina MBP is saying the battery needs servicing. I took it into the Apple Store and they ran diagnostics, and indeed it should be replaced.

Looking on Apple's website, this document seems to say it's $199 to replace my battery:

https://support.apple.com/kb/index?page=servicefaq&geo=United_States&product=Mac notebooks

In fact this was something I had researched before buying my MBP, because I knew the battery wasn't user replaceable, and $199 was a cost I was able to tolerate.

However, the technician at the store told me it would be $310 to send it for repair at their depot because the battery is glued to the top case, and so the top case also needs to be replaced, hence the added cost.

This doesn't make sense to me because if a battery replacement requires the top case to also be replaced, then why would Apple's website say it's $199 to replace the battery, when a $199 replacement is not at all possible?

I called the store and spoke to a rep, who said, "it's because your top case is damaged, because your battery expanded and damaged it." I told the rep that's a perfectly fine explanation if he can tell me how they were able to determine my top case was damaged and the battery had expanded without opening up the machine and taking a look. He was unable to answer that question, and passed me on to someone else.

The other person who answered the phone told me the $310 option was offered to me because it's $199 to replace the battery and $100 for the labor, which is $299, and for 10 dollars more, they can send it to the depot and be able to repair something else if necessary, so "it just made sense to go with the $310 option."

This is still quite an unsatisfactory answer to me because I haven't seen anyone mention that there's a $100 labor fee to replace the battery.

Has anyone had their battery replaced on their Retina MBP? What was your cost? Did you have to pay labor or replace the top case?

Thank you!