Do they? I hadn't found any specific requirement within the rules to the effect that once the jurisdiction of the independent tribunal has been invoked, the parties can't, so to speak, un-invoke it in the event of a settlement, though TBH I haven't looked that hard. If it's there, it's there, but it's perhaps odd that the rules would deliberately draw a distinction between disciplinary hearings and say rule X arbitrations where a consensual resolution of the issue would be as contractually binding as the original agreement to submit to arbitration.
My overriding feeling when Masters was saying 'it's in the IC's hands now' was that he was largely saying 'get off my case' to the redshirts (and Tottenham). That said, that's in no way evidence based, it's just what I thought at the time. It is however interesting (if this is indeed the case) that the PL didn't discuss a plea-bargain with City before charges were brought, especially if following the bringing of charges they lose the ability to control that process (though the IC would of course have been overwhelmingly likely to ratify any compromise that wasn't too one-sided.)
My recollection is that there was almost universal agreement amongst the media at the time the charges were brought that the real motivation for any charges to be brought at all was pressure on Masters from the usual suspects. The fact that they were so sensationalist about the bringing of the charges - charges going back to Mancini's time, the number of charges, the leaking to the media before the decision was made public etc - always seemed distasteful and did nothing to dispel the theory that this was aimed primarily at placating the redshirts (and Tottenham).
When you stand that alongside issues such as the undisclosed access that Liverpool and United were given to the applicants for the position now occupied by Masters (who actually arranged that, given that Masters was the acting CEO at the time?) the PL's opposition to the Newcastle takeover (which Newcastle themselves believed was coming from the same quarter) the swiftness with which the PL moved after that takeover to introduce APT1 and the decision to charge City in relation to eg matters such as an alleged breach of UEFA's FFP rules when CAS had acquitted City of that, and it raises serious and profound questions about the independence of the PL.
Not that you will find (m)any journalists writing about any of that.
At the end of all this, there's one hell of a book to be written about it all...