Besides staying clear of the fuse plug in the rim, it's partly because the sidewall of the tire is the weakest part of the carcass, so that a rupture from overpressure from overheating means most of the force goes sideways when the tire is stationary. The key word is "stationary".
When the tire is spinning, centrifugal forces mean the tread lets go from the sidewall all the way around, and the bits all go perpendicular to the axle, but when sitting still, it mostly goes sideways.
A secondary factor is the rims themselves. Aircraft wheels are built in halves and bolted together. They have to be made that way to ensure that there is enough overlap of the edge of the rim over the bead to prevent the tire from being forced off the rim by side loads.
You don't mount the tire the way a car tire is, by stretching the bead over the rim using a bar or in a machine. You place each half of the rim into the tire from each side and bolt it together.
If you disassemble an aircraft tire by unbolting the wheel halves and forget to release the pressure in the tire, you get a nice surprise when you remove the last fastener (this happens with forgetful mechanics removing light aircraft tires from time to time).
Anyway, this means that if the wheel itself fails and breaks into pieces, the large chunks of metal will go sideways, mostly.
Bottom line is with a stationary tire, the heavy structure of the belted tread acts like a containment structure to protect you, so you take advantage of that.