OK I used to work alot with hitches, trailers, brake controllers, weight distribution kits, 5th wheel hitches, trailer brakes, etc... etc... etc...
Just because you CAN tow something doesn't mean it's A safe or B not causing some sort of damage.
Dakota should be fine with a supra, the main reason they balk is the weight ratio. And yes, it's purely for insurance reasons in most cases, sometimes it's in safety reasons.
That being said, I'll explain some things about towing - none of this directed at the OP, it's just to get rid of some mis-information.
If you have a hitch on your vehicle that says XXXXlb capacity, it doesn't mean that is the vehicle capacity. Check your owners manual for TOWING capacity.
If your vehicle says your GVW is XXXXX that does not mean you can tow XXXXX.
Hitch balls are NOT universal. There's 3 main sizes, 1 7/8", 2" and 2 5/16th", there's also different size shanks on balls, usually 3/4" for a class 2 up to 3500lbs, 1" for class 3 5000 and 1 1/4" shanks for a class 4 up to 7500-10000. There's some odd-ball sizes as well but thats the major ones. If your reciever is 2" ball and you're using a 1 7/8" ball you're in danger of disconnecting while driving down the road ( cross your safety chains when hooking them up, it may save the trailer/load in case something like this happens ).
If you have a hitch installed CHECK ALL THE BOLTS. I don't care if it was professional, mistakes happen, check em and re-tighten em before/after your first tow.
" my small truck can pull a full car trailer with a buick roadmaster on it! " Sure, but you're also lifting the weight off the front wheels of your vehicle and reducing the control you have over steering in emergency situations. You're also overloading your suspension as well as most likely your transmission. Whats that burning smell? That'd be your transmission. You are most likely also overloading your brakes.
Towing capacity is based off MANY factors, transmission strength, braking strength, suspension strength, engine strength, vehicle weight vs. trailer loaded weight, tongue weight of the trailer, if the vehicle/trailer is equiped with trailer brakes/brake controller, is a weight distribtion kit being used, the list goes on.
Anyway, this is just information for you all out there. Take it how you want.
Murd