Insulated or not, if a toilet is repeatedly flushed with cold water in a high humidity, it will eventually get cold enough to cause condensation. The modern toilets are much less prone to condensation for 'normal' use, since the cold incoming water gets diluted by the room-temp water that's left in the tank from a flush. Flush it before it can warm up, and it gets colder, regardless of the insulation which only slows the transfer of heat, not stop it.
If you flush often enough, then the only way to resolve this is to use tempered water (i.e., mix some hot in with a special mixing valve) to keep the incoming water above the dew point, but for many, one of the new low-flush toilets resolves the problem without doing anything else.