While I'm not arguing with you Rob, the fact is that many Hiltons will offer you the ability to change your rate to a lower rate, and when you show up at the Hotel they pretend they have no clue that you changed your rate. I've had a rate go from over $200 a night to $73 a night, and even with both sets of paperwork the front desk was calling me a thief and a liar for trying to get the $73 rate. I had to go to the business center with Mister gonna pocket the difference, log into my Hilton account, and show him on screen I was confirmed at $73.
Yes there are many people who get hotels mixed up, or try to compare prices from one to another, but there are also way too many instances of the Hilton Reservations system not passing along rate changes to the Hotel, or the people at the Hotel pretending not to have them and the desk people trying to get a much higher rate then what it should be.
That's why the only safe way to do it is to book the lower rate and cancel the higher one. No arguments, as it is a different reservation number.
In my mind, it happens way too much to be an accident, I believe many people don't argue for the money and somebody is making money off this.