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For any type of off-road use I would think that the tire should be at least 16+ inches wide for that wide of a rim. I've seen 12" wide rims on 15.5" tires and they had problems with rim bead protection (dirt and sticks getting wedged between the bead and rim) and the tires not staying seated as well as a narrower rim.
I have a set of 15x12 8-lug rims with 38x15.50R15 Swamper Radials. Can't say I've had any problems, but I haven't done anything hardcore with these tires.
I run 40" boggers on 15x12's. Haven't had any problems with bead retention or sticks and junk getting wedged into 'em but I only have 2.5 runs on them and they've stayed aired up to 9-10 psi.
i plan on running my 33x12.5 on them until i get my new tires. it should be alright though shouldnt it? cuz my buddy runs 31x10.5 on 15x10 rims and hes had no problems. and we've abused his truck quite a bit on the trails.