However, you tried to prove this by counter-proof.
Actually, no. The whole presentation of the counter-argument only attempts to prove that that line of counter-argument (which has been put forward in a few variations) fails. It doesn't attempt to prove Perl Unparseability. If that was your expectation I can certainly see why you saw it as falling short. My presentation of the counter-argument is like an exposition of a variation on the Sicilian Defense intending to show a chess maven why he should never play it.
Arguably the post might have been stronger without it. I've dumped it into a "readmore".
The proof is given in three forms in the TPR articles. The strongest form is the one that uses Rice's Theorem. The other two may be considered explanations intended to help those trying to understand why Perl Parsing Undecidability is provable.