Can't comment on the Beerstones but regarding the CO2, yes, as we know there are different levels of CO2 in the beer dependent upon temperature of the beer. Colder beer will retain higher levels of CO2 than warmer beer. This is why, when priming, it is important to factor beer temp for the sugar calculation. When you take a bottle of beer that has been conditioning at 70+ for a few weeks and then open it warm there is the possibility that the bottle will gush because the CO2 has not been full absorbed into the beer (it may happen, it may not). If the beer is then refrigerated for a few days the beer will absorb the CO2 more readily and stabilize in the beer.
This is all my understanding as relayed over the years by people more knowledgeable than I. I only bottle and always have and these are also my experiences.
This is not how it works. When priming it is important to know the highest temperature the beer got to, as that will determine the co2 still in the beer. If it hit 72 and you bottle it at 60, it will not have magically absorbed co2 back into solution at the 60 level. The open beer on the counter overnite will not regain it's carbonation by putting it in the fridge. Pressure is the factor you are missing.
At a given pressure, a beer at 40 will have more co2 than a beer at 70. If I have a properly carbonated lager and an ale served at 35, they will not have the same co2 level because they are the same temperature. The lager will be at a higher pressure and therefore have more co2 in solution.
Also when you are naturally carbonating a beer the co2 is being produced IN solution, not forced into solution. When the pressure in the bottle equalizes, the co2 in solution can no longer escape and remains in the beer until that pressure is released. When you chill the beer, pressure drops as temperature drops so there is no more co2 "forced" into solution. It is the drop in pressure as well as the colder beers ability to hold onto co2 which helps to "stabilize" the beer and make it easier to pour, as well as a couple other factors.