Mech mods can have wires. Someone, somewhere, just up and "decided" that they don't like wires and they pretend that any mod with a wire is not a mech mod. It's wrong.
Although you may have a personal preference for no-wire mech-mods....any contact is really a "wire". Some are solid wires (like the pins in a button switch) and some may be stranded wires so they can re-position the switch away from the bottom. Regardless, it's in essence a conductor wire.
The original "mech mods" we used to build were DIY e-cigs....all mech....from 2xAA boxes. With a wire of course. All the current went through the button but through wires too. That's not cool for today's high-amp stuff. But in the old days, it was a quick way to DIY an e-cig for a few bucks.
If you think about it, your house has more watts running through it at any given moment (through wires) than any e-cig. And you seldom have to maintain them. That's not to say people haven't done stupid things and under-speced or over-watted a wire in an e-cig or house.
It's probably better not to have "a wire". But, it's wrong to say an e-cig with a wire in it isn't an mech mod or isn't "full mech".

and opinion.