They Don't Need Much to Watch You
If the FBI gets even the smallest, most meaningless tip on you, they're going to start watching you. They need to make sure that they have all of their bases covered. Even if the claim turns out to be false, they believe that every claim and tip is worth investigating. This type of investigating has helped stop tons of disasters in their tracks.
Using Satellites
The Simpsons portrayed that classic "FBI" van with the giant satellite on top of it due to rumors back in the day. The FBI actually uses satellite-equipped vans for surveillance, so The Simpsons' commentary wasn't too far off! Naturally, they are not permitted to use satellites to spy internationally and they always need a warrant.