I'm sorry, I did not read all the other answers. But here is more crazyness

    DynamicModule[{button, x = 0, ff, `},
     ff := (++x);
     var = Hold[x];
     var2= z;
     button = Button["setX", ff];
     Dynamic[Column@{button, x, Hold[x], Hold[x], var, OwnValues[ff], z, var2}]
     ]

-> Hold[FE`x$$213]

-> Hold[FE`x$$213]

-> Hold[x$314] 

-> {HoldPattern[FE`ff$$213] :> 1}

-> FE`z$$225

-> z$1236

Conclusions: It is possible for a variable to point to the wrong thing, like with var, or var2. ff does point to right thing, but it's code gets evaluated. Probably: The pointing to the wrong thing is **not** caused by the `DynamicModule` changing it's x all the time. I suppose it really wants to evaluate the code attached to symbols and not have it refer to any of the used symbols.

Also note

    DynamicModule[{gg = 0, x},
     OwnValues[gg] = {HoldPattern[gg] :> x};
     Dynamic[{OwnValues[gg], Hold[x]}]
     ]

-> {{HoldPattern[FE`gg$$270]:>FE'x$$270},Hold[FE`x$$270]}

but

    DynamicModule[{gg = 0, x = 0},
     OwnValues[gg] = {HoldPattern[gg] :> x};
     Dynamic[{OwnValues[gg], Hold[x]}]
     ]

-> {{HoldPattern[FE`gg$$271]:>0},Hold[FE`x$$271]}


It seems it does matter if we set something using `OwnValues` or in the regular way, using `Set` or `SetDelayed`. Lastly, it seems that a function definition can even be changed afterwards, like in

    DynamicModule[{gg = 0, x},
     OwnValues[gg] = {HoldPattern[gg] :> x};
     x = 0;
     Dynamic[{OwnValues[gg], Hold[x]}]
     ]

-> {{HoldPattern[FE`gg$$312]:>0},Hold[FE`x$$312]}

Lastly, even this yields an error

    DynamicModule[{gg = 0, x},
     gg :=  x[[1]];
     ]

-> Null  (error)

But this does not

    DynamicModule[{gg = 0, x},
     gg :=  x[[1]];
     x = {2}
     ]

-> 2

`DynamicModule` even seems to track dependencies despite `HoldComplete`

    DynamicModule[{gg, x},
     x := (Print["x"]; {2});
     gg := (Print["gg"]; First@HoldComplete[x]; Print["ggDone"]);
     ]

-prints-> gg

-prints-> x

-prints-> ggDone

-prints-> x

-> Null

I am lost :). I don't think I like this much.