Originally Posted by Swiss Tony

My guess is that it's because those fare classes, if you click through from ITA to the actual rules, come back with a note about not allowing stopovers in HKG if you fly BA. (which I put in my previous post - now bolded).

It's possible that if you try to book the fare on Travelocity it will get rejected before the booking is completed. For something like this I really would suggest checking with a reliable travel agent to see what they can do.