Partly correct, yes, colder liquids will hold more CO2 in solution. This is the reason warm cola bottles will fizz much more than the same bottle cold when opened.
The amount of sugar used in the online calculators is based on the coldest temperature during fermentation. As the yeast ferment out, they will excrete CO2 into solution, and any excess gas that cannot be held will rise to the surface and vented.
When you cold condition after fermentation has finished, the yeast are no longer producing CO2 (well, not in perceptible quantities), so the drop in temperature, and corresponding ability to store more gas in solution, does not have an impact. There is nothing "forcing" any more CO2 back into solution.
So, the summary is, the amount of sugar to add should be based on the coldest temperature of your wort during fermentation.