If it were me, I would simply decline and ask them to explain why they may think it's an issue with my house. If they have no reason to believe it is a problem, and are just "checking to make sure," I would say, "thanks for the offer, but I'm all set."

Very likely, they won't even bother pursuing it, and have probably been instructed internally not to put up a fight with people who refuse. If they do, you can simply explain that if they can't provide a specific reason other than "checking to see if there is a problem" they don't need to inspect anything, and if they disagree they will need authorization from a court with a written warrant.

If they threaten to cut the water if I don't comply, I would first try to get someone in the town or city to resolve it, otherwise I would file criminal suit against them, since it is illegal to extort someone to give up their rights. If I went down that route, I'd be prepared to go without water for a little bit, stock up, stay with friends/family, etc. It's not likely to go that far, but if it does, the law doesn't stop people from breaking it, it only ensures accountability for breaking it. Worst case scenario, it has to go to a district appeals court, but since it is completely illegal to cut off a public service for exercising rights, they will be found in the wrong -- it's just a matter of time.

The above is a worse-case scenario, but it's something you'd have to be prepared for if you wanted to go that route. Again, I'm not suggesting this is the right choice for everyone, but it is always an option to exercise our inherent rights.