I need to win an argument about fixed gears

That's bollocks. You can do high cadence stuff and high resistance stuff on a geared bike.
Time riding is moot since it's all about what you do in x amount of time.
I can be lazier on a fixed than on a geared bike.. it all depends on what you want to do.

It's not about the bike.

True.

But in a way, its easier to do on a fixed. Also I'm pretty sure the lazy 'letting the bike push your legs around' is better than freewheeling, as I tend to get less lactic acid build up ( I may be imagining this), when I start putting in effort again.