I'm sorry I can't help but wow, that is one of the strangest problems I have ever heard of.
Was there a clause about the house being haunted when you closed?
Even if there was a leak, an ant can't possibly swim in 100+ PSI of water... scratch that, an ant cant really swim to begin with. At least not in an enclosed area with no air.
Now is this one of these
? Maybe there's actually a way they are getting into the faucet part itself. Maybe a small crack in a tile or something or whatever is behind it.