At 8 weeks, my Maggie had unlimited access to water. It is my belief that, barring any medical condition, a dog should always have free access to as much fresh water as he needs.
I did, however, take up the water in the evenings during our housetraining so that Maggie could make it all night without having to go pee. Worked well.
Is there a reason why the vet said the dog's water should be limited. I'm very suspicious of that. All dogs need LOTS of fresh water daily and if your dog seems thirsty, I think it would indicate that it isn't getting enough. Is there any sign of dehydration? Does the fur "snap" back to the body when pulled up? If not, then the pup is dehydrated and needs more water.
I'm concerned about such advice coming from a Vet.