I once booked a President's Suite at the MIA Airport Hilton that was listed for the same price as a standard double. At check-in the reservation had been modified to a standard double. Upon discussion with the front-desk and, after that, the GM I was upgraded to a JR suite on that stay, the reserved President's Suite on my next stay, and dinner for 2 was comped.

So, yes they can and will correct a mistake res, but in some instances (if pushed) they may make some accommodations afterwards depending on the property/GM.