I think I can picture the situation. In short, you have a raised floor in a basement, no? If I'm wrong, then I'm not properly picturing the situation.
With that, it's hard to say whether fixing/replacing the humidstat will solve the problem. It sounds like you need to do that anyways. If you didn't have or sense a mold / mildew problem before, then chances are that you still won't assuming you address the humidistat.
M / M doesn't really die unless you spray it with a mixture of 1 part bleach 4 parts water (at least.) Leaving it alone kinda sets it into dormancy. You could then begin experiencing dry rot which is the repeated wetting and drying action on wood. Kinda like rain and sun, rain and sun, and so on, over a long period of time. The only problem is: Even if you kill the M/M on or near the panel, what about the rest of the under-floor? Can you see any 'damage' or M/M if you bend down and look inside? If so, address that too. And to boot, who knows how 'far' the problem goes ...
I guess you will know if the problem is fixed if, after you replace the humidistat and kill the M/M, you don't see the 'problem' any more. How long you have to wait is anyone's call.
You said the 'space' is vented. Is it vented to the outside, or inside? If it's vented to the outside, I'd leave it along. If it's vented to the INSIDE, that just allows the M/M to 'enter' the house. IMO, that's not the way it should 'work'.
If the Inspector is the one you need to 'please', then ask him what needs to be done to satisfy the inspection. It's that simple. From there, you can negotiate w/the Sellers to see if they want to absorbe the expense of the fix, have $$$ put in escrow, have the expense taken off of the price of the house, or bag the deal all together. The IMPORTANT thing here is that if the Inspector is going to tell you what should be done, then you should get it in writing from the Buyers that when the job is complete, they will buy the house since the Inspector SHOULD give it his seal of approval. So, your NEXT move should be to retain a Real Estate Attorney. He/She knows how to write up these Inclusions/Exclusions. For the fee they charge, they'll review everything you give them BEFORE you sign. (That goes w/o saying.) Talk to friends and hire someone to look after YOUR interests. I wouldn't take a recommendation from the Seller's realtor or the Inspector. (They could be biased against you ...)