Haven't been able to try this, just passing along the info; looks rather time consuming, but could be worthwhile with a big price difference.
Six Continents
"Lowest Internet Rate, and Starwood's "Best Rate Guarantee" promise the internet rate is the lowest or the customer can obtain the lower rate AND 10% rebate.
First book on hotel web site, www.sixcontinentshotels.com,or website of individual brand. or www.starwoodhotels.com if the traveler finds cheaper rate elsewhere on same, date, the traveler must contact individual hotel directly, and that hotel must confirm the rate is available. The discount will then be offered the traveler.

My information does not state if one goes back to the internet or if the hotel takes care of the rate reduction and rebate.