Like I say, I think you are probably right, and Mark Hendrick MP seems to agree. But the evidence that the PL has actually been pressured into bringing unwarranted charges against is is (AFAIK) nonexistent.
The process, as I understand it, goes like this.
1. The PL decides to open an investigation. There will generally be some reason for them to do so, like a complaint being made that we have broken the rules, or (as in this case) something coming out in the media that, if true, would suggest that we have broken the rules.
2. As part of their investigation, they ask us for the documents they think are relevant to that investigation.
3. The PL rules say we have an obligation to provide those documents, but if there is some reason not to, eg they are not relevant to the investigation, we can choose not to.
4. The PL then decide whether to issue a disciplinary complaint about that, as they did in this case. If so, it goes to an independent panel. The panel then decides whether the information requested should be provided, because it is relevant to an ongoing investigation, or whether the club was justified in refusing to provide it.
So the answer to the question 'who decides' is ultimately an independent panel, but there are several stages in the process before you get there.