Do applicants have to pay separate fees to apply to two PhD programs at the same school? I initially thought yes, but it seems after some research that this is not true!

It seems the fee goes to the overall graduate school, not one specific department.

Can someone in the grad world back this up for me?

I would rather not send an email asking, may seem ungenerous.
I strongly suspect that you would have to file two different applications to apply to two different programs, and each application would likely require a separate fee to file. This is in part because you would have separate essays and letters of recommendations for different programs, each of which would require separate handling and consideration. 

If this is a hardship, though, some schools offer an application fee waiver to students who are of limited financial means, but you may have to contact the individual school to inquire about the possibility, because it may not be publicly stated that such an option exists.