Very interesting reading!
Kestas posted the correct way(s) to rotate non-directional tires, assuming that all tires are the same size.
Obviously, in cases where the front tires are smaller than the rears, you cannot swap front to back. As long as the tires are not directional, you should swap side to side in this situation.
There is no danger in X rotating radial tires. This is a myth. It is very advantageous, in fact, to use the tire such that it rolls in both directions. This evens out any heal-toe wear that can develop when a tire rolls in a single direction for it's entire life.
Heal-toe wear can cause increased tire noise (sounds like a bad wheel bearing sometimes) and an overall higher wear rate, resulting in shorter tread life. In extreme cases, it can even cause vibration felt in the steering wheel.
Tire shops are correct in putting new tires on the rear of the vehicle.
New tires generally offer better traction in slippery conditions. It is well known that understeer is a much safer and controllable situation than oversteer for the average driver. This is why vehicle manufacturers tend to design suspension components to bias the handling characteristics towards understeer. If the tire shops put higher traction tires on the front, the back end of the vehicle could come around (oversteer) and cause an accident. $$$ Lawsuit.
Tire shops are also correct(i.e. protecting themselves and the customer) in not installing a tire with a lower load rating than what original came on the vehicle. In many cases, the lower load rated tire may be able to handle the loads, but will require a higher inflation pressure than what is listed on vehicle placard in order to do so. Not a good situation for the average consumer. Underinflated, overloaded tires will fail.
This is a good time to remind everyone to check your tire pressures on a regular basis!! Running a tire low on air, even for a few miles, can cause permanent damage to the inside of the tire.
