can't get the gvwr math to work

1000lbs for Water and Gear is all dependent on yourself and camping style. The easiest way to save significant weight is to not fill the water tanks until you reach that last mile to your campsite. Bit more of work but you can save several hundred pounds right there (and get that Diesel). Propane as well, you don't have to go with two tanks filled if you limit your hot water and heat needs. For clothes, just as a guesstimate, maybe one person will have 50lbs of clothes, shoes and jackets and that is probably being generous. Food for a week for one person is maybe 20 to 30 lbs. Dishes, utensils, pots and pans, maybe another 20 lbs. Basically, if it is just you and you are not hauling kids or a wife, I think it is easy to keep your weight to a minimal amount to stay close to your GVWR.

In addition to truck camping, I'm an avid backpacker and one of the tricks of the trade is to get a digital postal scale and just weigh everything on your packing list and keep tabs of those weights. When your planning a trip, go through that list and check off the items you know you will need for that particular environment (hot weather gear, cold weather gear, etc...). I've never done this for the camper but it is one way to be able to objectively look at your gear and figure out where you can save weight if you need too.

That being said, GVWR is a topic of much heated discussion in the Truck Camper forums. Some swear to never exceed while others feel they are more like guidelines that can be tweaked with the appropriate modifications. I believe the truth is somewhere in the middle, as long as your reasonably close to your GVWR, your going to be fine. If you exceed it by significant percent (I'll let you decide what significant translates to) that you can start asking for trouble.

Having just done all the research to buy a new Ford, I can say that there are charts in the Ford towing documentation that calculates (estimates) the truck cargo weight based on chassis and engine. This particular chart (page 12 in the 2018 document) deducts the weight of the total number of passengers at 150 pounds each from the payload. By doing some simple math with the number of passengers you normally carry you can adjust for your situation.

Look at the payload sticker on the door jamb. The payload you'll have to subtract from that is everything, driver, passengers, etc. except for fuel.

You are confusing government taxation with real math.
We have a million (maybe more) topics about what taxes you pay v/s what are the vehicle real capabilities.

Double check the language. Usually they assume a single 150lb driver and no one else. There was a push a few years back to adopt an SAE standard that assumed two 150lb people but I don't think anyone adopted it for their advertising (reduces the ratings they can show in ads). Maybe Ford did change the way they calculate it...I've even come across adds that in the fine print leave the driver out, so it's the weight sitting empty with no passengers.

Are you accounting for misc gear added to the truck...bed liner, steps, trim, hitch, etc... Unless you get a stripped down work truck expect at least a couple hundred pounds added.

If it's the dealer telling you this, make them put it in writing in clear simple language that you load this camper and put 1000lb of gear in it, you can get in and drive off with a full tank of fuel and not be over GVWR. Then load up and take it down to a scale. If you are over GVWR, take it back and get your full refund.