I don’t think this is true at my kids’ schools which are similar to CA. If the kid is released from the obligation that is different.
I believe that the kids at these schools get a huge advantage from the very personalized college counseling. The admissions teams put a lot of trust in the LOR’s, and the counselors help the kids apply ethically (well other than the whole ethical question of providing some kids this help when public school students don’t get it) and strategically. When a counselor violates that trust and those ethics, it seems reasonable that the advantage goes away.
If the situation is as it seems, and there isn’t some other factor, then I think CA should probably fire the counselor, and that should restore Tulane’s trust.