MIPS I believe that's correct. There were two towing packages (not including dealer options). Class II or "heavy duty" included different axle gears (3.54?), transmission cooler, heavy duty battery, and load leveling shocks along with the larger hitch and trailer connectors. Also possibly tuning differences such as timing.
Dealers (and buyers) could generally pick and choose add-ons from the factory, or add their own equipment. It's very possibly your Eagle has a Class II hitch that's not factory, and a larger transmission cooler that is...or vice versa.
In case anyone is wondering:
Towing capacity on the Class I is approximately 2500 pounds, max tongue weight of 200.
Towing capacity on the Class II is approximately 3500 pounds, max tongue weight of 350.
It's very possible that if your hitch is not a factory hitch it may look like a Class II, but actually be a Class I. Hitch classes are dependent on their weight capacity and your U-Haul hitch (or whatever) may have a square receiver but only be rated Class I, so be cautious.