Without going into all the details of the situation: I sincerely believed my offer was very competitive for that candidate. It was a very substantial raise over his current comp, and the number I gave him was vetted by our recruiter as very competitive.

The difference also wasn't very large. As I said, had he told me about the other offer, I'd have offered him more, no problem. That's why I encourage candidates to negotiate in this situation. Just say "look, I really liked your offer, but I just got another offer for $X." Worst case, you'll get politely declined. If my impression of you was positive so far, I won't change my mind over this.