In this case, I don't at all think the controller was stonewalling the pilot about the number. If I'm busy controlling traffic, I'm not about to take my mind off controlling to issue phone numbers to pissed off aircraft, and I'm certainly not going to get distracted by engaging the pilot in an argument about what happend (which probably would have followed if the controller had issued the number).
It's not as if the controller thought that by ignoring the pilot he could avoid the situation completely. Every controller knows that there are multiple ways of checking which controller was working which position for every second of the day, and that all the ACC phone numbers are publicly avaliable from any number of places.
Yes, if the controller had a couple of minutes to spare, and wasn't that busy, he should have gave the pilot the number, but if I'm busy, that's going to be the last thing on my mind, and the last item on a long list of priorities.