The situation has improved dramatically in the part 91 world. If you received a 3rd class (including special issuance) within the past 10 years you can likely now do BasicMed as long as your condition is well managed. Might be worth looking into before the 10 year limit expires.
If they already have a non-revoked 3rd class from before, though, having used one not on this list may not prevent getting BasicMed. Even if you’re technically eligible for an SI you should just do BasicMed and not risk it if you don’t have to. Disclaimer: not an AME, YMMV.
This is clearly false. The limitations on BasicMed are different from those of a standard medical certificate [0], and have to do with your physician's medical opinion about your ability to operate a plane. There are a few conditions that specifically require a new SI [1] but this is not some pseudo-legal/badfaith game.