An unexpected diagnosis of anything is always unsettling, so sorry you are having to go through this. The link angelkin provided is a good one, and from some reading there and other reputable sites, I'm having a hard time reconciling what your specialist said with HPV. The rate of infection is so high, that any adult with HPV should not come as a surprise to anyone. Also, it's impossible to determine where you got it, so best not to even worry about that. From what I understand, it could have been years or decades ago. Young females are testing positive for HPV even prior to their first intercourse, so basically any sexual contact of any type can transmit it.
I'm no medical professional, but something isn't adding up here. Either it's not HPV like you suspect, she misinterpreted the vibe she picked up on, or you need to find another specialist. What is adding up is she's not comfortable with him/her, and no matter how this turns out, she should seriously consider finding someone she is comfortable with. There is a time for the holding your secrets close approach, but this isn't one of those times. Too, what kind of professional throws out something like that and then doesn't follow up with anything else and leaves you guessing and trying to figure it out on your own? I understand they may not know for sure at this point either, but they should at least run down the possibilities for you, and if they won't, then again, time to find one who will. Going through these things is hard enough without someone who is supposed to be helping the situation but instead is making it more difficult.
Like most things in life, swinging is a calculated risk. If just walking away from it would reduce your stress and worry level, then it's certainly something to consider. On the other hand, if it's something you both enjoy, then maybe just taking a break to give the facts time to work their way to the top and fill in the blanks to allow you to make an informed and calculated decision would be a good approach too.