After a bad rainstorm in January I started to get extremely bad static on my line and it was unusable. I contacted Verizon to schedule a repair. A week and a half later the technician came out, did some work and appeared to fix the problem. A day later it rained and the problem returned. Another repair request. Another week and a half. This time, the repair person called me and said that there was some issue with water getting into the line. He thought the problem was in my neighbor's yard, but he was having an issue getting into the yard. I'm not sure why as she is home all day during the weekdays. He also mentioned that he made some sort of repair with a circuit in the office. Again, the problem "seemed" to be fixed but soon returned.
Rain and older copper telephone service have always been an issue with one another, so it might be an especially hard problem to fix once and for all. If you want to do "your due diligence" then double check with your neighbor as to when a good day and time would be where the technician could go in their yard. Get their number for contact, and when you file another report make sure to give them both your numbers, and let them know the neighbor is giving access and right of way to Verizon to do the repair. If it's FIOS then it would be unusual that the problem is outside (not impossible) but real unusual. SO if FiOS is in your neck of the woods, you may want to just upgrade, it will likely fix your problem if it's really outside in the yards and the streets.
Also - when the static comes back, MAKE SURE it's coming from the street. It most likely is, but go ahead and make sure. Take your phone to where your outside Verizon box is located, open it up and plug it in (standard telephone test jacks are inside the Verizon box, they sometimes call it a NID)
If you get static even when plugged in at that box, then yes it's an outside problem that they need to fix.
If it's clear when you plug in at that box, then they don't need outside access, the trouble is inside your house.