I think you two are disagreeing about terminology. You're the ecpert in the field, which (correctly) makes you more sensitive to terminological distinctions.

What's not disputed I guess, is the commonly (to CS-educated engineers) held notion that FCT is a high-profile math problem that was solved/proved by intensive automatic means rather than a human written proof, and that that raises questions regarding the meaning of "proof".

At least that's what I took home from it.