> You cannot get a warrant without probably cause that a crime has been committed. So asking for a warrant to search your computer is literally asking to be charged with a crime.
That is just completely 100% wrong. Warrants are not (or at least, shouldn't be, your mileage may vary based on your local authorities) issued like candy. Prosecutors and judges issue warrants when there is probable cause to search in the event of a crime being committed by you, or simply being committed within an area to which you have access that the public does not. That does not mean you are being charged with a crime. I would agree that more often than not, if you are having warrants issued for searches of your home or business, a criminal prosecution for you is probably not an unreasonable thing to be concerned about, but these are not the same thing. One absolutely happens without the other all the time.
> If you can just agree with their legal team on the stipulations of the search and confirmation, you can't be charged with further crimes if they find anything
This is the same fallacious thinking as "If I've committed no crime I have nothing to fear from being searched," and that's not the point: the point is it is your right to privacy that they are demanding they now have the right to encroach upon to ensure the secure and to-their-satisfaction destruction of data they erroneously sent you which cannot be performed without some element of highly invasive search, and also cannot be requested without the implication that they don't trust you to have deleted it.
This institution regardless of your individual opinions on it does not have your interest at heart: their negligence has placed the two of you as legal entities on opposing sides of a legal affair that can incredibly easily escalate to a conflict. Your lawyer is your FIRST call in this situation, and after that, you shut the fuck up and let your lawyer do their job.