...be sued or will that be covered? under my landlord's home policy?

Depends on why he fell and if the landlord has a home insurance policy. If he fell because of his own faulty equipment, then he can only sue his company. If he falls because of something that is yours, then you are liable. But, if it has something dealing with the upkeep of your landlord's home, then the landlord is liable.

Your landlord is responsible for keeping a home insurance premium and ultimately liable for that type of lawsuit. If you pay renters insurance, that is just covering your personal property.......One of the few benefits of renting!.....Technically, the landlord would then have recourse to sue you for breaking the lease terms if it does not state it's ok to install a satellite dish. Chances are that the Direct TV sub-contractor is already insured against accidents (as long as the resident is not negligent).