> If “Parsing is validation, but validation is not parsing” is true then it is also true about compilers.

This is a false statement, considering that the cases where something is validation but not parsing may very well lie in the complement of the set of compilers to the set of all computable functions. The converse statement that if this were true about the smaller set (of compilers), it would also be true about the larger set (of all programs) would on the other hand be correct.