Actually I guess the answer is in your boss's words:

3.He's removed them from existing tables to change things and it's caused data corruption that was only noticeable weeks or months later, on high-traffic/ high activity sites, so he'd rather not use them.

FKs removal does not change data, yet, if someone runs queries against the DB, like your boss did, how does RI at the application level prevent corruption?
Something not to discuss, but remember he had to remove the FKs to change data, and possibly in a manner that wnet against the rules implemented by the droped FKs.