It might be some weird fetish or something, though it's a pretty weird thing to ask/do. Maybe she just wants a guy to share her fetish with? So it might be a way to proof you could be into that. It's something that's easier to ask on the internet first, rather than asking a guy she's dating in real life.
But the question is if you would be able to handle it, I would listen to my mind and pride in this case. But it's your life, ''your'' girl. But using it as a proof for trust? If i wanted my friends to prove our friendship by letting me fart in their face, I would't have as many friends as i do now. Even though i still know i can trust them without farting in their faces haha. Farting in face =/ trust ?