No, it is quite incoherent. Specifically, it fails to even offer what any physical theory must: a quantitative prediction. Compression, in your view, can be allowed to produce variable amounts of heating, for the same change in density. Since you aren't making a quantitative prediction, how is what you are saying even testable?

(The answer is that compression produces a specific amount of heating when it is adiabatic, and additional heating comes from dissipative processes that are occurring alongside the compression, but that are not themselves compression.)