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.