It's more of a general statement to keep all "like" tires on each corner of a 4WD or AWD vehicle. The reality is, many of the AWD systems can handle mismatched tires and some systems aren't bothered even by different sizes of tire front to back.
On the permanent 4WD systems, the limitation typically comes down to the transfer case.
Tread design is likely not a factor at all for the mechanical aspect of a given vehicle drive system however mismatched tread design can result in complaints from the vehicle's electronics if the vehicle senses the ever-so-slight differences in rolling resistance or perhaps differences in tire design as a result of speed rating.
For whatever it's worth, of all the AWD and 4WD vehicles I owned, the only time I've ever replaced all 4 tires due to a tire failure was with the permanent 4WD system in my (then) 2005 4Runner.
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