That is incorrect and you need a credible source. You do need a license to hunt coyotes, private or public lands.

http://wildlife.state.co.us/SiteColl.../smallgame.pdf

I copied this directly from page 2 "Purchasing a License" of the on-line 2012 Colorado Hunting Regulations:

6. You can hunt coyotes without a small-game license during big-game seasons if you have an unfilled big-game license for the same season and unit. You must use the same method of take for coyotes as your big-game license allows. Once the big-game license has been filled, hunters must purchase a small-game license to continue hunting coyotes.