Fred,
Ok so I swapped tires onto a different set of rims and took some measurements. For reference here's what was used:
Rim 1: velocity A23
Rim 2: Neuvation M style std 19mm width rim
Tires: vittoria Rubino Pro 23mm
I used the same exact tire for both measurements.
A23+Rubino Pro: 25mm wide and I had 11.8mm clearence from top of tire to a flat point on brake I used as a reference.
19mm wide rim+Rubino Pro: 23.6 mm wide, 11.2mm clearance to the same point.
So the tires do sit wider and flatter than on conventional rims but not as much as they would have us believe. Hope this info helps you make your decision.