Could be the pan under the evaporator has holes in it. Did the technicians pull the coil to check for holes in the pan? At the very least, after blowing out the condensate lines they should have poured water into the pan to check for proper drainage and to ensure there were no leaks in the evaporator's drain pan.
It could also be an issue with not having a trap installed in the condensate line. On some sytems that have the condensate line and evaporator coil on the suction side of the fan, no trap installed will allow the water to be sucked back into the pan and eventually may cause the water to spill over the pan. Having the trap installed insures the water will drain properly. It could also be an improperly installed trap that allows air leakage. To give you an example, if the condensate comes off the pan and goes to a tee (used often as a port for blowing or cleaning out the line) and the tee is not capped off when not being used for cleaning purposes, this will allow air to be sucked back through the tee and prevents the water from flowing through the tee and onto the trap.
You were correct in not running the unit as water can drip down into a fan motor below the pan and cause it to short out.
One other issue that comes up from time to time is the inability for water (condensate) to drain or trickle down the face of the evaporator coil. This is usually due to dirt blocking the fins of the coil and the condensate accumulates on other portions of the coil and when it hits the blockages of dirt or other debris, it doesn't perform its usual capillary action and follow the fins down into the drain pan, but instead stops, accumulates and then falls straight down into the lower sections. Check the coil's fin surfaces for dirt or other debris. If present, have the coil cleaned.