I can confirm that 32c tires will fit without fear of rubbing. Which is opposite of what I said months ago. Not sure how I messed that up, but perhaps I was using the wrong wheel/tire combo. Using 32c tires with anything less than 23mm internal wheels will most likely cause rubbing since the tires will have more of a bulbous effect. My original test was with 20mm internal wheels.
Wheels: 30mm external, 23mm internal
Tires: Conti GP5000 STR 32c, measures about 32.5mm at the tire