I agree with what yu are saying. I believe what yu see.
However I have seen several of these "pictured " Fully tubular hitches (aftermarket) on 04-07 HL's.
Ask DrawTite what application
IS the one in the picture for!!!
Check with Reese Hitches.
The full tubular Hitch is a stronger design. I would not get one that is notched out with a welded in U bar that surounds the exhaust. It looks terrible.
BTW, on
01-03 HL's, the OE hitch is not fully tubular as I just discovered. It is a different Toyota Part number.
It has the U bar around the exhaust.

The exhaust pipe sits lower on these early HL's.
Maybe DrawTite has a mistake in their application. Maybe yu just spoke with an idiot. Maybe they have superceded the 01-03 application to the 04-07 HL's. This happens on occasion.
My thoughts.
Yu may have to look elswhere. Have yu considered a
used OE tubular hitch for the HL? If yu find one...yu can even repaint it if needed. Just an economical alternative to OE new.
LT