I have to say I didn't know that, but just looked up the message I got when I registered. Here is what I got back:

"You are now registered to receive 4,000 bonus Starpoints. Simply stay at Four Points by Sheraton hotels three times by June 7, 2005"

It doesn't say "any". Then I click on the "official rules" I get this:

Terms and Conditions
Offer is valid at U.S. and Canadian Four Points by Sheraton hotels April 12- June 7, 2005.
To register and for complete details visit fourpoints.com/launchflyer or call 1-877-782-0020.
* For a list of locations that have the new Four Points by Sheraton Four Comfort Bed, visit http://www.fourpoints.com/bed.
Limit: 12,000 bonus for nine eligible stays.
Must be a Starwood Preferred Guest program member to receive Starpoints and all Starwood Preferred Guest terms and conditions apply.
To join, and to see the complete terms and conditions of the Starwood Preferred Guest program, visit SPG.com.
Offer may not be combined with other offers.
Void where prohibited by law.

When you click on the link, you then click on participating locations.

I dislike the Four Points and usually don't stay, but I did three times. Until I saw your post I assumed it was any Four Points too, but luckily the three I stayed at were on the list as participating.

FWIW I don't think it was obvious that you had to look at some link and make a special note of which ones were participating. If there were only certain ones they should make it obvious in an email or when you register so that people know not all locations are covered especially when it looks like a lot of locations aren't participating.