IIRC the headspace limit on the 32 is the same as the 30/30, maximum 0.007". I'm pretty sure it's a proof house requirement so if the gun has been recently proofed it should be OK. FWIW I've measured the rim thickness on a bunch of cartridges since I bought my 30/30 and they've varied by as much as 0.0015"
The cases I've measured were norma, W-W , winchester, Remington, Federal, Speer and hornady. I bought a bunch of once fired cases from bullet cache in hythe which is why I had such a variety.
IIRC Federal were the thickest but can't remember the thinnest.