Thanks for the info everyone.
Talked to my service advisor, and he confirmed that the part number is the correct TP6-100A hitch. They seem to be convinced that Honda's site has an incorrect picture. I asked that they contact Honda America to let them know and confirm, which they said they did. In the meantime, they will remove my hitch tomorrow and refund me the $800 they charged me at time of purchase.
I'm bummed that I won't have a nice, hidden, factory hitch, but I'm not paying $800 (including wire harness, and install) for something that doesn't look better than a $170 aftermarket hitch.
I just sent Honda Customer Service a Twitter message asking for confirmation on the hitch not being hidden, referencing this forum. I hope they have some good news...