Official inspections can peek and poke the nukes a bit. But they can't really tell exactly how good the maintenance is. Similarly for a spy.

You are right that wholly non-existent nukes would be harder to fake. But covering up bad maintenance isn't quite so hard.

In your point's favour: Looking at the Russian military budget, they do seem to spend a lot on those nukes. Of course, funds could still be siphoned off. But having a big budget is at least necessary, even if not sufficient.