I can see why you're worried. Some people do grow up to be obsessed with urination, usually in a sexual way. But in those cases, the reason can usually be traced to spanking related to potty training, since spanking can stimulate nerve endings that trigger sexual arousal. I am making the assumption that this is not the case with your daughter. If it is, I would recommend therapy.
And if that isn't the case, then I'm not sure there is reason to worry just yet. I know it seems quite odd, maybe even shocking and disgusting. But in fact, for a seven year old who worries about accidents, the whole idea of her body creating this liquid and her having to work so hard to control it can be quite challenging. If she felt very pressured to be perfect about potty training, that anxiety could all be coming up again now. And if she's been to a doctor recently who had her pee into a cup, that could easily make her more aware of her pee.
So what can you do to help her resolve whatever is worrying her?
Obviously your daughter has some shame about this whole issue, or she wouldn't have said "nothing" and then begun crying when your husband confronted her in the bathroom If your husband had not been taken by surprised, he could have had a lighter touch, and maybe gotten more diagnostic information. In such a case, he might have sat down on the edge of the tub, smiled at her, and said "Pee is cool, huh?"
She might have answered "Yes, it's such a beautiful gold color...Does everyone's " pee look like this?" or "Doesn't it seem like magic how this washes out our bodies?" or "I like the way it comes out warm on my clothes" or "Yes, but it smells funny...Do you think I'm sick inside?"
The goal of such a conversation is to understand what her fascination is, and to begin the process of melting away her shame. That helps melt whatever that sticky knot is that is obsessing her. You can still have that conversation.
But first you'll have to help your daughter dissolve her anxiety about the issue. The way to do that is to be playful about pee. Anything that gets her giggling. Make pee jokes, pretend you're going to have an accident, talk about how much you love to pee -- whatever gets her giggling about it. Once she offloads that anxiety by giggling, she should be open to a conversation.
As far as "trusting" her to spend the night at a friend's house, I think that's the least of your worries. If you don't find a way to make it safe for her to tell you what's going on with her, then how can she trust you to tell you anything that feels vulnerable to her? Once you do have that conversation, you should find that shining the light of day on her "obsession" helps clear it up.