My brother and I can't figure out how it would damage anything as both the diff and manual trans are closed fluid systems that dont use a pump or filter. If the drive wheels are on the ground, what can go wrong? There seems to be those who think it's a bad idea all over teh interwebz.
Wont the trans heat up even less than when it's in driving use? It's not electronically controled.

MKIII Turbo Supra 90'

The only thing i can come up with is that instead of the pinion driving the ring gear, the ring gear will be driving the pinion. The alternate faces will be in contact, like decelerating while still in gear. Only outcome is maybe a little extra wear and tear? I could see the trans heating up at all considering it will just be the output shaft spinning, with no load on it. Give it a whirl!

That's a good point, but by this time the other sides of the ring likely have wear as it has plenty of miles on it.

The MKIII is going to be low enough with the front bumper that you're not going to want to dolly that with the nose down, and putting the drive wheels on the ground with the car off can wreak havoc with the fluids (depending on the transmission, some won't pump enough fluid to keep all the bearings lubricated when the car isn't on.) You could disconnect the driveshaft to be absolutely sure, and it isn't that bad of a job (one of my best friends has a '90.)

Quick question - why not a flatbed?

He's calling tomorrow to see how much the flatbed trailer is. I wasn't aware the manual had any pumps to be used while driving, what pump are you refering to?

I'm not the foremost transmission expert, I was just relaying information gleaned from the many, many times I've had my car towed. From my basic understanding, each of the gears on the shaft going to the differential is mounted on bearings - these bearings are lubricated internally so that when the car is off the wheels can spin freely without turning over the entire transmission (allowing the car to coast, essentially, and the car must be in neutral to do so.) Some transmissions lubricate these bearings with the spinning of the shaft going to the wheels, where towing wouldn't be a problem because it would be able to pump lube (that sounds dirtier than it is) to these bearings. However, some transmissions lube these bearings by the shaft coming from the motor, so when there is no load coming from the motor, these bearings can heat up with the rear wheels spinning even when the car is in neutral.

So, to answer your question, an internal pump is used, but don't quote me on that because I'm not positive that's right. Long story short, I'd go with the flatbed or disconnect the driveshaft to be 100% safe.

I've got literally thousands of miles on my VW from being flat towed up and down the east coast. I think it might be different with a front engined rear wheel drive car as my mom's 2005 Mustang specificially states in the manual to disconnect the driveshaft when towing, but it's automatic.

Some manual transmissions do have fluid pumps for cooling purposes, not lubrication purposes, to my knowledge.