I'd say you had that correct!
I found it very difficult trying to drag an AI with the HD pneumatic wheels through sand which is why I originally got the Trax cart. I haven't tried it with the TI but Bob's response shows that it's not easy. The new style Trax2 balloon wheels are much more versatile than the original Trax1 tyres which couldn't even cope with an AI. They were really only useful for the standard kayaks.
Until Hobie release their TI specific cart the Trax2 cart is my choice because you can add the HD wheels to it easily if travelling a distance on hardpack. You can't add the balloon wheels to the HD cart.
You may have seen my post where I added an extra set of wheels to the Trax 2? viewtopic.php?f=69&t=34910
With this cart even my wife can drag our loaded TI through the sand!
It also rolls better on hardpack. It is important if carting a fully assembled and loaded TI to ensure the load is spread across the TI hull. I've used webbing, others have had success with shaped foam or even the Hobie cradles.