The sun is the source of all energy in the system.
The starting point is that whatever happens is a consequence of more energy or less energy entering the system.
If you propose that the Earth cannot become a snowball without reducing CO2 or recover without increasing CO2 then that is your hypothesis.
While we are about it how sure are we that it did ever happen ?
We are moderately sure that 'slushball' conditions happened with evidence of cyclical glacial deposits in places that would have been at low latitude at the time. The evidence for a complete snowball is patchy at best.
I never said the Earth cannot become a snowball without reducing CO2. Where did I say that? Reduced levels of GHGs would help for sure but the initial trigger is more likely to be continental configuration (most continents near the equator), changes in ocean circulation, orbital cycles and a slight tendancy towards glaciation anyway as the sun was dimmer 600 million years ago.
I would certainly not say that only large concentrations of greenhouse gases are needed. To simplify, let's say you need 100 units of forcing to get out of a slushball state. Your GHGs have built up to 75 units (arbitrary number) but can't really get any higher. You need to wait for other conditions, solar output, orbit etc to be more favourable and provide the extra 25 units. As soon as it starts melting you probably get a dump of methane into the atmosphere providing an additional kick.
That's how I see it anyway. I wonder if anyone will attempt to run this on a modern model with all their chemistry and biosphere components.
BTW Stephen, did you answer my original question that led to this discussion? I asked "Are you saying that if we had the oceans but not GHGs the Earth would be about as warm as it is now?"
Just to clarify, this means imagine that water vapour and clouds have no radiative effects either. Essentially dealing with the approximation that leads to the conclusion that the greenhouse effect adds up to about 33C.