It's a property based on the premise that not just any made up number is equally good as a valuation...

The very definition of "valuation" points to the underlying "true" part -- valuation means an attempt to guess at the value of something.

It might not be possible to have a perfect guess (because nobody has all the data or knows all the future events that might affect it), but it's very possible to know a valuation if BS and critisize it.

Would you buy a Denny's dinner in rural Nebraska for 1 billion dollars?

By asking a Scotsman.

And yet, if one avoids this supposed "fallacy", the logical conclusion would be that no group has any definite properties, and everything is interchangeable.

So, yes, there actually are things that "no true scotchman" would do (else there's no reason to invoke a group named "scotchmen" at all).

Sure, but the restrictions are 1. be from Scotland 2. be human

In the case of OP, valuation is simply what the market will pay to own the stock of a company. Sometimes it coincides with what any individual will pay, sometimes not. There is no sort of magical intrinsic value to a company. All we are really doing is arguing over the definition of valuation.