Regarding the adiabatic lapse rate: there *are* thermodynamic assumptions that go into that calculation. One of them is that there are adiabatic vertical air currents; the calculation that gives you the lapse rate is basically the calculation of how much a parcel of (high-altitude, low-pressure) air will heat up when descending and being compressed, or vice-versa. If air is moving vertically, then you *will* have this heating effect from standard textbook thermodynamics. It gives you a relationship between the derivatives of pressure and temperature---it doesn't give you the temperature itself. You apply this relationship to (a) hydrostatic equilibrium and (b) surface temperature and *all together* these constraints fix the lapse rate and the scale height. They're not independent.
But Zig is not, as far as I can tell, claiming anything different. He's not claiming that basic thermo "magically" tells you the surface temperature or the scale height. He's claiming that there's a basic thermo lapse rate which, combined with the hydrostatic equilibrium equation (which includes the total mass of the atmosphere, which differs from planet to planet) and some temperature setpoint (which depends on radiation and whatnot, and differs from planet to planet) tells you that a massive atmosphere has higher lapse rate than a low-mass one. Sounds good to me.
But note that this is not the only way for an atmosphere to behave. An isothermal atmosphere is also a perfectly good solution to the thermodynamics. The stratosphere is another perfectly good solution.