You can tow an AWD DSM. The trick is to have all four wheels off the ground while it is being towed. This can be done using a flatbed tow truck, or putting the front wheels on dollies.
The reason that AWD DSMs should not be towed with two wheels on the ground is the limited-slip differential (LSD) which is present on many AWDs. The function of the LSD is (surprise!) to allow a limited amount of speed difference between the front and rear wheels.
[Please note that the operation of the LSD has been simplified here for the purposes of discussion. This is not a dissertation on the LSD itself.]
Under normal driving conditions, the front and rear axles rotate at the same speed. (This is what differentiates AWD from older 4WD vehicles - on 4WD vehicles, it is assumed that the front and rear wheels usually rotate at different speeds while the 4WD is engaged.) During this time, the LSD does no work, and is 'open', providing no coupling between the front and rear wheels of the car.
The LSD is a viscous (fluid-based) device, and contains no mechanical interlocks. When one set of wheels begins to slip, plates in the LSD rotate at different speeds. The speed difference creates friction, and therefore heat, in the LSD fluid. When enough heat is generated, the LSD fluid abruptly changes state from 'open' to 'closed' providing a semi-solid junction between the two plates. With the fluid now 'locked' the plates are forced to rotate at near-equal speeds, which is turn forces the axles to turn together. When the slip condition disappears, the LSD quickly loses heat and returns to an 'unlocked' state.
So, the raison d'etre of the LSD is to prevent excessive wheel slip between the front and rear axles. The only problem with this occurs if two wheels are forced to slip, while the other two remain stationary. This occurs, of course, if two wheels are on the ground (rolling) and two are stationary (lifted) while the car is being towed.
In this scenario, the LSD will quickly build up heat and 'lock', attempting to rotate both axles equally. Unfortunately, it is unable to do so, since the stationary axle is locked securely into place by the tow operator. The other option is to halt the rolling axle, but the LSD does not have the strength necessary to resist the force provided by a tow truck designed to pull much larger vehicles. So the LSD plates continue to slip, even when the LSD is 'locked'.
When placed into such an impossible situation, the LSD does the only thing it can do - build up heat until it self-destructs. The tow truck driver, driving a dually burdened with the added weight of a 3000 lb car, is unlikely to notice either the extra resistance provided by the LSD or the lack of resistance once the LSD burns out. By the time the car is again dropped to the ground, the LSD is literally toast.
This situation can easily be avoided by only towing the car with all 4 wheels off of the ground. The exact method used is not critical. And no, it isn't going to hurt the LSD to load the car - technically, the front and rear axles are never going to rotate at exactly the same speed during driving, so the LSD plates are always rotating at slightly different speeds. Obviously, this doesn't hurt it, since it runs in 'open' mode normally - the problems occur when it is 'locked' and still cannot equalize the axle speeds.
Those interested in the exact operation of the LSD can read all about it in their technical manual (you do have one, right?).
Those interested in the details of the AWD system should read Eliot Lims Introduction to AWD Systems.