That is an assumption on Heidegger’s part, that what we perceive cannot be the way it is. He may be quite incorrect about that. The thing itself can be subjected to a criteria of truth, what is, i.e., being itself or reality itself. To say, as you do below, that truth is “only” a property of language is to assume that statements about reality necessarily don’t or can’t match reality.
This is only true if the words have no actual referent in reality, which is entirely assumed by your nominalistic world view. No one, likely not even you, really believe that when statements or claims are made they are not made “about” a corresponding entity in reality but only “about” other statements. Pardon my bluntness, but that notion borders on psychotic delusion.