The base is made out of ptex and yes, you can absolutely melt the base if you apply too much heat.
Sounds to me like that shop fucked up your board and they owe you a new one. They're trying to pass off the blame and play dumb, but they know exactly what happened.
"People say that marijuana smoking is going to get in the way of my career. I say to them that on the contrary, my fighting career is getting in the way of my marijuana smoking." -Nick Diaz