it's not a mathematical or logically defined tech
AO is very clearly defined, mathematically-speaking. Lambertian diffuse is computed by integrating lighting * occlusion * cos(theta) for all directions about the hemisphere, and AO approximates this by integrating the lighting and occlusion factors separately and then combining afterwards. The fact that it's an approximation doesn't mean that we can't reason about when it makes sense to apply it, and what will produce results that best simulate real physical phenomena.
you define Lambertian lighting, by using occlusion and say occlusion is defined? I think that's not the way definitions work in math.
but you are right, AO approximates occlusion, and that was my point also. if you had a specific light source, you could separate lighting from occlusion (in that case it's commonly called shadow or radiosity map) and we'd all follow well defined algorithms.
and if there would be a clear definition of AO, then every tool should generated the same results, but the results of AO baking (and even in interactive rendering) varies a lot.
if you'd just go for the generic occlusion (aka not per light), indoor would be always just black. that's why baking tools usually have some tweaking values to set the range you sample the occlusion and in what way the angle/distance/density will be mapped to 0-1 and depending on how you apply those baked maps, artist will tweak the maps in a different way.
It's even more vague in screen space effects.
that's why I'm suggesting to go for the optically most wanted results than for some theoretically most convincing argument that looks inferior. We can somehow define what we want to achieve, but we strive into approximations, into theories and it ends in a pool about what most think would be best in theory. what if the 'best' we vote looks worst in the game he makes?
That's why I suggest to vote for the visually nicest results and he should post the 3 versions (probably just a change of 3 lines of shader code).