"Our former system administrator is extremely uncooperative and very confrontational" or "we need to decrypt valuable customer data that we can't afford to rebuild and this is driving us towards bankruptcy" are the kind of words that make most educated people very much unwilling to help, no matter how much money you promise them ;).
It's not a matter of principle, it's a matter of headaches. It's very unlikely that a customer like that would pay enough to make it worthwhile.
There’s plenty of people willing to work at any price point. Just because a $200/hr consultant dismisses the request, a $10/hr one can probably still figure it out.
However if the alternative is bankruptcy I think there IS money to be spent on the solution.
That is also assuming you have the time, the resources, and the general knowledge to pick out a great contractor whom you can trust with the security and safety of a critical system.
^ This. When someone approaches you saying things like "our former sysadmin is confrontational and unhelpful", you don't just have to solve whatever problem the guy who ragequit can't solve. You also have to undo the damage made by the asshole who's contacting you after they tried to solve it themselves, and sometimes by the one or two unqualified people they tried to hire afterwards.
You know how employers are skeptical to hire people who start the interview by saying how awful their last/current workplace was/is? Same here. I've definitely met hundreds of developers or sysadmins that I wouldn't trust, and whose services I wouldn't recommend. I've definitely been wrong and hired some of them myself. But I would never say something like that in public. At the end of the day, who's the smartass that hired these people in the first place? I get it's frustrating but such is life, you still have to be professional about it.
Plus, 200 USD/hour for a quick fix looks like a great deal, but even if the fix itself takes one hour, it's rarely a one-hour job with customers like these. You routinely end up invoicing for less time than you spend deflecting their attempts to negotiate the bill, explaining why it took one hour and itemizing it, and getting them to pay the stupid invoice.
It's not a matter of principle, it's a matter of headaches. It's very unlikely that a customer like that would pay enough to make it worthwhile.