This is very, highly unlikely. Communication protocols are robust enough for the signal to travel many miles through all sorts of interferences. It would have to be some extraordinary source of EMI for it to cause enough disturbance in a (properly installed) coaxial cable. Something like heavy metalworking equipment perhaps or very intensive welding operations. Running 24/7, too, which in itself is rare occurrence. In any case the fault would still be on the cable co for pulling their cables too close to such source. And for not properly grounding it, too.
Anyhow, this excuse is almost comical. I am assuming their service is not delivered over fiber optic, in which case it would be simply insulting, since it's not physically possible.
If you want to give them a benefit of a doubt, ask again what they actually meant. But chances are, if they were being serious, it is not EMI (ElectroMagnetic Interference) they are talking about.