Math isn't mathing

Thanks guys! My concern is not the truck, it is the trailer. We are looking for a new trailer and having a hard time finding what we want. The Genesis comes the closest but once I looked at cargo capacity I'd be really close if not over, and that is only a small RZR and dirt bike. We boondocks 90% of the time so definitely will push cargo capacity. My big question was why 7000 lb axels but then limit cargo capacity to 14K when you will have almost 3K riding on the truck. I get they have CYA allowance and they under build these trailers. I really wonder how many people are hauling big 4 seaters in this trailer and are way over weight? It's a shame how tall the manufacturers do this.

OP you’re tracking correctly. 
However the simple posted capacities for (most any) RV are simplified to reflect the safe load capacity knowing they cant account for all the variables of how it will be loaded. 
But your math is correct. In that if you add full water (huge tank btw), full gas (not a lot of weight) and your roughly 1600lbs of toys you are at the rating almost spot on. With no other gear aboard. 
And a resi fridge so plan on full hookups, 24/7 generator screaming or more batteries for a legit inverter setup. That alone would send me packing from this camper. But maybe you never go where there’s no hookups. 
What isn’t explained is the water will about balance the toys load and if you’re closer to maxing out the tires and axles you will likely be ok.  However you don’t want to do that balancing act nor does anyone. 
Just like other campers different toyhaulers have different ccc numbers. 3600 isn’t bad. Some are over 4klbs and some are considerably less. 
Your math is fine. 
That model is not really suited to hauling a big 4 seater sxs or your 2 toys which weigh about the same as a big 4 seater. Just because it’s a toy hauler doesn’t mean it will haul “every” type of combo of toys. 
PS, based on your fridge type, and my comments regarding that, either you’re looking at the wrong configuration for your use or you will likely have water at the campsite hookup so no need to pack a cistern full of water. Gotta figure in your intended use. 
Lastly, when we had a toyhauler I looked at several when shopping and can say they do a lot to ease the “cracked frames and overloaded axles” concerns that are common with many non toyhauler trailers with very little ccc on paper. The frame on our 2017 Torque was STOUT. I would have had no issue loading full water and a big SxS with respect to the frame. 
Bottom line is you just learned that just because it’s a toyhauler doesn’t mean it can universally haul the heaviest toys you can put in it without exceeding some rated capacity or other. 
Broaden your search and see if you can find one similar with a little more CCC maybe. Although you’ll probably only find around 500lbs more than the camper in question. 
Every single RV is ideal in some scenarios and a compromise in others. Doesn’t matter if it’s a 43’ tag axle pusher or a popup tent trailer or anything in between. 

Here's mine (loaded):

I have 3 7000 axles but I'm sure my rig isn't up to handling whatever cargo 21000 lb would give. Other parts of the trailer reduce the capacity.

Hitch weight (or pin weight) is roughly 20% of GVWR. 20% of 14k is 2.8k, which is slightly more than their claimed 2610.  Depending on how they balanced the load (assuming they loaded one to full GVWR) they may have weighed the pin at this actual figure, and/or they are providing the best estimate for what weight the pin would have. Use this figure to guesstimate what the load would be on your truck.  Your truck's Payload will be reduced by all passengers, gear stored in the bed, hitch, etc.  Make sure you'll still have ~2600lbs left for the pin weight.  However, be careful to check your truck's Rear GAWR.  Almost all the pin weight (95%--just assume all) will be on the rear axle. Weigh the truck alone to get your rear weight (load on rear axle when unloaded) and subtract this from the GAWR to get your max available load capacity for your rear axle.  Hope that helped--we are new to this ourselves, but, my math background, hours of research, and experience as a long haul driver helped me grasp all this over the last couple months. 

Deleted

Just a guess but I would assume the manufacturers have to account for things like the actual chassis strength in the ratings. Just because the axles are rated at 7,000 each doesn't mean that the frame is strong enough to be rated to more than 14,000. On top of that the manufacturer has to factor in a safety margin to keep people safe and more importantly reduce their liability risk. 

Welcome to the world of campers and RV's where most are overloaded and manufacturers lie about dry weights and load capabilities.  I'll bet your hitch weight will climb once loaded too, putting alot more weight on your truck.  I cringe when I see some of these monstrous 5th wheels and trailers on undersized SRW trucks, hopefully you have at least a dually 3500.