Seek truth: I agree with the other posters in what they say about Witness "thought/philosophy" in regard to relations between boys and girls. The Witnesses are very controlling and manipulative in this area; they are very reactionary in regard to inter-gender relations.
But I am not sure if this was the reason - or the whole reason - why the girl said "no" to your son's invitation to the prom. I intend no disrespect toward you or your son, but perhaps she isn't all that "into" your son. Maybe she simply did not like him enough, and would have said "no" even if she were not a Witness. After all, you provide very little detail; you just mention that your son invited the girl to the prom, and she "flat out" refused. I have to say that it is her right to refuse. You give no details. Perhaps she is going, but with another boy. Are we to assume that because your son did invite her to this socially significant event, your son and the girl were on at least very friendly terms? I mean, what was their relationship before he invited her? Were they familiar with each other at all, or is she a pretty girl that he had admired from afar? Did your son have any right to reasonably expect her to say "yes"? Did it come as a total shock when she said "no"? Like I said, the important thing is their relationship/friendship before he invited her.
What I am saying by no means implies that I disagree with the other posters; they are correct in their assessment of Witness "culture" in regard to relations between the sexes. Given that, I wonder why, if your son knew the girl was a Witness - and presumably he knew her enough so as to be aware of this fact - did he even invite her to the prom in the first place, given the Witnesses attitudes toward such "worldly" events. In any case, I think that it would serve you better if you provided a little more details about the situation.