It's not just that the paper/canvas/leather won't melt, it's that the heat transfer through the container (to the water behind) is fast enough to prevent it from reaching the temperature at which it would be damaged (or at least lose integrity). Porous materials have the added advantage that water soaking through it will also keep the surface close to water's boiling temperature.

Only experiments will prove it, but I suspect that the wall thickness and low thermal conductivity of polycarbonate (and the fact that the polycarbonate is not porous) would combine to make it unusable for boiling water over an open flame.