Absolutely correct there Don. In this instance, Utah has decided to recognize any Concealed Handgun Permit from any state which has authorized such carry.
It gets tough when you're dealing with cross country travel though. In some states they have requirements regarding the length of the required class. If for example "State 1" requires an 8 hour class time with "XYZ" curriculum; "State 5" has a requirement of only 6 hour class time with "X and Z" curriculum. "State 5" would recognize the "State 1" permit, however "1" would not recognize "5" because the requirements have not been met.
Disclaimer: Just goes to reinforce the need to keep up to date on CCW laws, and not just in your own state. For anyone traveling with their gun, CCW or not, save your self the possible cost, headache, and legal issues.... do your research.