Drilling holes in the wall's not the worst of it: When Verizon comes, they insist on cutting the copper connection to your apartment, and therefore, in your case, the whole building. What's so bad about that? Well, copper lines run on their own power, but when you get fiber, for some reason, it needs an external power source to continue phone service. In case of a power outage, you get an 8-hour battery backup, and once that's gone -- no dial tone until the power comes back. What happens if there's an ice storm and the power's gone for days? Answer: One full complex of pissed-off tenants, and one even more pissed-off landlord!
Actually, because Verizon wants to cut off the copper (technically they don't have to -- they can keep customers on copper for phone calls and DSL -- but they want to cut it off, anyway), they might have to get permission from your landlord to get FiOS into the building.
So threaten to move out unless she allows FiOS -- nah, that won't work, she'll just find someone else to move in your place. Insist on her to consider putting a D* dish on the roof where nobody will see it (if she's that vain); if she still says no, you might as well find someone else to live.