Oral hsv1 is linked to Bell's Palsy, not genital. Herpes infects nerve groups, so if you have genital herpes, it doesn't affect your face, and vice versa.
There are other causes of Bell's Palsy, though, like Lyme Disease and Epstein-Barr, which causes mono. Yes, hsv1 is the cause for a large number of cases, but it's not the only one.
The other thing to note is that the IgG test can miss 30% of hsv1 infections.