That doesn't sound right to me. I'd first check the charge in the front compressor. Sounds like they are thinking the heater is on when the AC is on, with each counteracting the other. Even if that were the case, the problem wouldn't be the core itself, but the control valve. And I believe that is under the hood, not under the dash (unless it is the electronics in the dash). When the front AC is on, see if you get any frosting of the lines under the hood. If there isn't any frosting, the problem is the AC, not the heater core. The compressor may not be engaging, it may not be working at all, or it may have lost its charge. You should be able to feel if the compressor kicks in or not.