..you'd have to run a guaranteed clean version of the hash-checker, not the copy from the usb stick.
i think this is where we diverge into the superspy paranoia vs real world risks.
while it is conceivably possible that someone could write custom malware that would infect and modify the hash checker to trick it into reporting fake hashes, this is just so unlikely as to make it not worth worrying about (you could also make that quite hard by putting some protection on the program itself).
so yes, the malware could infect the hash checker (though you could do some stuff to make that hard), but it's not going to make it report false hashes, so it would still do it's job of reporting an infection.
and after it did, you would not trust the files on that thumbdrive to be safe any more, as they would have been trojaned, including the hash checker.. but that's ok, the point is to DETECT the infection.