I suck at logical thinking, so I'm not saying against you, but here's what I've done several times:

Brew a beer, ferment it etc and drink it.

Then to double the batch size I've brewed a High Gravity version of it, and watered it down 50% before fermentation. Same OG and after a few try and fails.. same FG.

So same OG and same FG. The watered down version tastes nothing like the non watered down version. The watered down version is WAY more drier on the tongue. Even after upping salts etc.

I must believe that there's a different amount of dextrins, as I have to mash 4C higher to get the same FG in the diluted version.

Your situation is somewhat different but let's try and dig deeper. If you have the same ABV you'll have the same mix of water and alcohol giving you your base density, which will be lower than 1 as alcohol is lighter than water. What gives you the actual FG is this base density + X amount of residual extract per unit of volume. So basically for your two beers:

FG1 = Base_density1 + Extract_density1

FG2 = Base_density2 + Extract_density2

But we know that FG1 = FG2 so let's call both FG and we have:

FG = Base_density1 + Extract_density1

FG = Base_density2 + Extract_density2

But we also know that Base_density1 = Base_density2 because both beers have the same ABV so let's call that Base_density and we have

FG = Base_density + Extract_density1

FG = Base_density + Extract_density2

We can strike out Base_density without changing the truth value of the equation and then we have

FG = Extract_density1

FG = Extract_density2

Both terms on the left being equal it follows

Extract_density1 = Extract_density2

Q.E.D.