I don't think the intent is to have you book at a higher price. The intent is to get the booking and collect the fee. And they just don't care that they can't process corporate codes.

They are misrepresenting things, and asking about a discount code probably should get you forwarded to the hotel (or their corporate call center). It can get a little hairy when Hotels.com (or whoever) has a lower price or more rooms available than the hotel directly (sometimes the Online Travel Agencies will commit to a number of rooms over a time frame, then they have pricing autonomy and exclusive availability; probably not happening in covid times though)