Not sure if a dealer or someone else told you the Thule 963 Spare Me spare tire mount bike rack was not compatible with the 2006 Honda CR-V, but in any case that would be incorrect. The Thule 963 Spare Me does in fact fit the 2006 Honda CR-V perfectly. If your spare tire has a cover on it you'll just need to remove that first to gain access to the mounting points located in the center of the wheel. Also the Thule 963 Spare Me adjusts for spare tires that are off center so the bike rack and bicycle still ride centered and don't stick out too far on one side of the rear of the vehicle. More info on the Thule 963 Spare Me spare tire bike rack can be found here...
http://www.orsracksdirect.com/thule-spare-me-spare-tire-mount-bike-rack-963.html
Also you can check out the Thule Racks online fit guide on the site to verify that this spare tire bike rack does in fact fit the 2006 Honda CRV.