I am not sure whether there being a witch hunt against the club at all affects the substance of the PL's case against City. The allegations are effectively that the club fraudulently filed incorrect accounts and did some other stuff against PL financial rules. Not sure how there being a witch hunt or not is relevant. The club either did those things or they didn't irrespective of whether there was a witch hunt or not.
But if we like conspiracy theories, how about this one:
The club knows there has been some correspondence between the PL and a club that, for example, the PL has insufficient evidence to prove the most serious of the 115 allegations, but they are going ahead anyway because that is what the other club wants. The club don't want to disclose the provenance of the correspondence (for one reason or another ;) ) but they want to raise it with the panel.
What does the club do? It counter-claims on an issue that will require the PL to disclose all its correspondence. They can identify all the incriminating documents in that case, and, once documents have been submitted in one, they can use them in the other. If the PL doesn't disclose the correspondence the club knows about, they are in bigger trouble. Win-win.
I like a good conspiracy theory, me :)