All I can tell you is that we usually drink our soda pop warm and from 2 liter bottles. And keep the stuff at room temperature.
Just looked at a diet Coke bottle and saw no refrigeration dictum.
Without sugar, and with the acidity added by the carbonation, would think storage at room temperature for a reasonable amount of time would be OK as far as bacterial growth goes.
Heat is the enemy of carbonation, it drives off the carbon dioxide, so perhaps the reason they state that is to maintain the carbonation (the screw caps are not always perfect at keeping in the gas).
However, don't know what sodas you are referring to.
Am just speculating here, but we have never had any problems keeping ours at room temp.