I think I found a fix for this (on PC anyways), after TONS of tinkering (I played through the beginning crash scene more times than I can count...)
Just like @jnoble20987 I was having issues with ME2 in game thinking I had all the achievements, despite having never played the game before, and not having any achievements in the EA app. After messing around with the save files in documents, I also noticed that the issue seems to be tied to the "TrilogyGamerProfile" file found in "Documents/BioWare/Mass Effect Legendary Edition"
Once you start up ME2 and get past the beginning scene, it generates this file so that you can "Choose bonus powers" and such when you lock in your character. From testing, this file seems to be tied to the EA cloud somehow, so the workaround is to not be connected to the internet when you start the game. However, due to always online BS, the EA app wont work right if you are not connected (at least from the new EA desktop app, not sure about Origin/Steam) so... you need to kill the internet after launching, but before character lock in.
TLDR:
1. delete the "TrilogyGamerProfile" file found in "Documents/BioWare/Mass Effect Legendary Edition"
2. Start up the launcher for the game.
3. Once the launcher is good, but before clicking "Start" for ME2, disconnect PC from internet.
4. Start ME2.
5. ...
6. Profit?
I tried this with a fresh ME2 save, and an imported ME1 save, and it seemed to work both times. No starting bonuses/powers/resources, and I did finally get the "Missing in Action" achievement in the EA app because the game doesn't think I already have all the achievements anymore. I have also launched that same save after doing this workaround, but while connected to internet, and it seems to still work.
Caveat. I have not actually progressed the save to be able to check achievements in captain's quarters yet, but I think it's working. I'll update if something changes.
UPDATE: when I got to the captain's quarters, surprise surprise, all achievements again unlocked. I deleted the trilogy gamer profile again, as well as the "GamerProfile" at
"Documents/BioWare/Mass Effect Legendary Edition/Save/ME2", started the game in offline mode using the workaround from above, and captain's quarters no longer had the achievements unlocked. So, looks like the only way to avoid this issue is to always make sure there is no internet when the game launches (and probably the whole time you are playing).