GPS determines a solution for position and time simultaneously. It requires 4 satellites to solve for 4 unknowns (X, Y, Z, t). If you know your position you can solve for time using only 1 satellite, but a watch is always moving so it's position won't be known.
Edit: I would welcome corrections though if I am misunderstanding. Perhaps if you're not interested in precise timing you can read the satellite time from the broadcast signal?
Edit 2: OK, I think I understand your point now. The satellites broadcast their timestamps directly. To find a precise position / time you need to find a correction to the receiver clock. But if you don't need a very precise time, you can just use the satellite timestamp.
