The "fictional" Rainbow Six crew operates world wide and is made up of several multi-national Special Operations Units. The FBI HRT only operates for domestic situations, that's our soil. The do shoot drills, entry drills, and attend the same courses as both SEALs as well as the uber elite Delta boys. So in that respect I'd concur with your assessment. There is another unit that very few are aware of that have international juristiction. The CIA has a unit very much like the HRT nicknamed the Farm Boys. Do some homework and I'll think you'll find them to be much more closely related to the Rainbow Six thing. Be forewarned, you won't find much about them.
US Army SSG. 82nd AB INF