When you say that something has a towing package, it is implied that it is an additional upgrade package, beyond standard.
The person you are talking to at the dealer does not know what he/she is talking about. They are at a desk with a book or a computer, but no actual knowledge of the product.
Since 2002, all Explorers/Mountaineers come standard with a class II (1¼") receiver, and enough structure and cooling equipment to handle up to 3500 lbs. Regardess of engine or drivetrain, from the factory, if you did not get the HD trailering package option, you are limited to 3500 lbs. This also includes a 4-pin flat harness for trailer lights, which you probably have found by now.
The HD Class III/IV towing package includes an upgraded 2" receiver. I think you also get upgrade engine and transmission cooler (not sure on that part). If you have the V6, you get different axle gearing good for somewhere around 5000 lbs tow rating. If you have the V8 (2002-2005), you get the axle upgrade and somewhere around 7100 lbs. 2006-2010 V8 with tow package gets the 7100 lbs without the axle upgrade, due to the standard 6-speed transmission. The HD package also includes (in spite of the clueless dealer guy) an upgrade to 7-pin connector for lights, trailer brakes, and an aux 12V power line.
So if you have the 1¼" receiver, regardless of your drivetrain, you are limited to 3500 lbs. But it sounds like you have a trailer that you want to tow, that has a 7-pin harness.
1. If this trailer is more than 3500 lbs loaded, then you do not have enough truck for the job. You can't swap out the hitch on this truck since it's welded in. You would have to add a lower-mount hitch and end up with 2 receivers. But that still leaves you with only 3500 lbs towing rating. If you have the V8, you would at least need to add more transmission cooler. If you have the V6, you would also have to upgrade your axles from 3.55 to 3.73 gearing.
2. If this trailer is 3000 lbs or less, then you are probably find to tow this trailer without upgrading the hitch. Class 2 is good for up to 3500 lbs. Just go to etrailer.com or any RV shop, and get the 7-pin connector. You will not use all 7 pins. Just cut off the existing 4-flat connector, and wire into the proper pins in the 7-pin socket.
3. If this trailer is 3000-3500 lbs, it's a gray area. You'd need to check your combined vehicle weights against the GCVWR (check your manual, or the Ford Towing Guide online).