This is all more or less correct, but is not at all the reason why hotel offer you to enter your IATA number.
The reason is comission. If I'm a travel agent and I book for one of my customers directly through the hotel website they will be able to identify my agency with my IATA number and bank my comission. But they will show exactly the same rate, no matter if an IATA number is entered or not. It's just a comission thing.
Travel Industry rates are handed differently (either through a promotion code or with specific rate codes through GDS, i.e. Amadeus).