The stock carrier is capable of holding a 33" tires, just not capable of holding it safely while trying to drive the vehicle. A lot also has to do with the weight of the tire and rim. The lighter the better. I have done a lot of tires over the years and some hearly need a forklift to pick up and others are one handers, size is not the determining factor oddly enough. Stock Superdutys are amazingly light while some half ton trucks are not. So just saying you want a 33" tire back there isn't a good realistic benchmark.
Personally I had issues with a 31" on a steel wheel on the stock carrier. This was simply driving around town. I ended up rigging a bungee cord as a backup plan to the latch. when the latch would let loose (which it did often) the bungee would catch it and slam it back into the tailgate. That was my cue to go back and reset the latch again. On the trail I was doing the fix every 20 minutes, and by trail I mean a dirt road you could drive any normal car down on a good day. Thankfully my latching issues forced me into a real bumper mounted spare tire carrier before I had body issues. I have seen Broncos that went and super reinforced the latch only for the bed corner to start coming loose from the quarter panel.