I fixed the issue doing the following.
I made of copy of the CFIDE virtual directory in the root of the web site and that did not help. Then, I manually recreated the CFIDE virtual directory back to the default settings and rebooted the server and the CFTREE started working.
Rather than doing this - it's a substantial security risk which has been exploited a few times recently - yuo're better off to just put the /CFIDE/scripts dir somewhere within your website and use <cfajaximport> to tell CF's JS code to look there instead of /CFIDE/scripts.
If you insist on exposing your /CFIDE directory, make sure you're fully patched, and follow the CF lockdown guide (except for the bits about securing /CFIDE, obviously ;-)