In our area, the City is the Water Company. The City owns the pipe from the main to the meter, just like they "own" the sidewalk and from it to the street, and the tree that they planted there too. Can't talk them into mowing it though, darn it.
If their pipe has a problem, they fix it. You do not pay for this except in your quarterly bill for water service. But you pay for fixing everyone else's pipes in that bill to so it all works out. They leave it in good condition but do not replace expensive sod and maybe a few tractor ruts, but, all in all, they do a good job and you really can't beat the price. Check before you spend your money on something a plumber can't legally do anyway.