TC,
12 years ago, after RVing for 3 years without a towed, I wanted to tow a Mazda Miata. The Miata owners manual said the same thing, "not recommended" without specifying manual or automatic transmission.
I bought a 2000 Miata 5-speed manual (already out of warranty) and sourced a replacement transmission for $250 and I have the ability and tools to replace it if necessary. I made a $250 gamble.
Being an engineer, I designed and fabricated my own baseplate and tow bar and towed that Miata over 35,000 miles.
I towed a 2010 Miata over 25,000 miles and have now towed a 2012 Miata over 20,000 miles.
In the ensuing 12 years, I have helped more than 125 other Miata owners to get their cars flat towable. In that time, I have NOT had ONE report of driveline damage from flat towing a Miata.
My point here is that Lawyers, NOT engineers, speak for auto manufacturers and lawyers do not like ANY liability.
I know that a Miata is a rear wheel drive car and not what you have and there may be precautions that you can take (e.g overfilling the transmission) to tow yours.
Personally, I would check with Roadmaster, Blue Ox and Demco to see if any of them make a baseplate for your car. If any of them DOES make a baseplate, you can rest assured that SOMEBODY is towing them.
Tim