Could insulation around copper pipes cause condensation problems?
Insulation on pipes should prevent moisture in the air from condensing on the pipes, by preventing the air from coming into contact with the pipes.  What you are experiencing could be caused by a few things.


Insulation was not installed properly, and is not preventing the moist air from contacting the pipe.
Condensation is forming on an un-insulated section of the pipe, and is flowing along the pipe into the insulation.
The roof is indeed leaking.
A leak has formed somewhere along the pipe (remember, there is water in them there pipes).


But why don't I see the problem when I remove the insulation?

Removing the insulation may be allowing the moisture to evaporate before it can build up and cause problems. the insulation could have been preventing evaporation, which allowed a noticeable amount of water to build up inside of it. Once the insulation reached its saturation point, the water had nowhere to go but onto the floor.