After going through several other tests with EA support (I've even tested the game without updates and even on a 1st generation xbox360)... they still have to escalate the issue... no solution yet.
During these tests there is one test I've made which clearly states that this is not related to each person discs or specifically to disc 2... nor even related to their save games (being corrupted for instance).
1. Start game with disc 2 (game not installed)
2. It asks for an update. Download it if not done already (if you put disc 1 it also asks for an update even if you have done it already with disc 2 or vice versa)
3. Then start New Game (don't try to load any save game)
4. As expected it asks for Disc 1, but the same issue here. It doesn't recognize it ☹️
My personal guess, is that we'll need a new patch because there might be some conflict with the API used within the game to check discs.
It certainly worked before, for people playing the game probably before 2013. According these posts dates, after some xbox software updates (dashboard, system, etc.), it no longer detects the same way as before... or so it seems ☹️
I'll still have my support case being analysed from specialists, and I'll post here its updates.