Would that cover a trespasser who was injured?

They pulled the gas meter and fire captain explained what happened and that report will say tenant is at fault-accident.Thankfully no one was injured not even the dog I filed a claim with my insurance  and tenant has renters insurance with same insurance company as me-State Farm she also filed claim of some sort or notified them. 

BUT, you have to have liability insurance in case if someone injures at your property you will covered. 

The pet happened to be a pitbull who jumped my fence and injured the neighbors dog.

That said, the STR's violate the terms of my lease, so in the event one of my guests gets injured in my property and sues the landlord,  I am going to assume they'll come after me.  

Recently, a socket caught fire in my rental property and the tenant was injured while putting out the fire.

Say soon after the take over, the tenant sues because he was injured and got sick.

If you go it alone and miss a rule, and somebody notices or one party is injured(financially or otherwise), you could be held personally liable.

Nobody ever injured themselves with free wi-fi...

Please keep in mind Med pay coverage is where you ask the insurance company to voluntarily pay for someone's injuries, so the injured party does not need to sue you under the General Liability policy.I have personally used this coverage on my homeowners policy.