For the repair extension program for the 2011 MBP, they had a diagnostic program that they ran to identify whether or not the computer would qualify for a repair (if I recall correctly). I would have thought they would have had a similar diagnostic program for the 2012/2013 program. It might be worth your time to research if that's the case.
But let's presume there is no diagnostic program that Apple can run and that they might do something if you can "show proof". According to the repair extension program, you have to have one or more of the following conditions:
- Distorted or scrambled video on the computer screen
- No video on the computer screen (or external display) even though the computer is on
- Computer restarts unexpectedly
You haven't mentioned that condition 1 or 2 happens (or does it?). Which leaves condition 3. For that, you should look for the kernel panic logs because of the different types of logs that I've seen on the Apple, that tends to be the best one at identifying what happens when the computer crashes. Not every crash will produce a this type of log. (If your computer doesn't restart unexpectedly (crash), and none of the other conditions apply, you will have a difficult time trying to get a free repair.)
In the Console app, this should be under "System Reports" or "System Diagnostic Reports" or something similar and will start with "Kernel" and end with ".panic" or perhaps ".gpuRestart", although the .gpuRestart log could be a software issue (I've had those happen and it was an OS-related issue) and is not as helpful as the .panic log. On the disk, this will be in /Library/Logs/DiagnosticReports". Now, if the tech who helped you didn't go looking for this, well, they weren't that helpful. If you have this type of log, post the results here. If you have multiple, just post one and mention that you have more and if that log isn't helpful, we'll ask for more.