i think his point was with regard to the "perma" in permafrost. Strictly speaking, permafrost is not a seasonal feature. It may be short-lived on a human lifespan basis but it isnt seasonal with respect to melting.
I think you are referring to soils/tundra that undergo a seasonal thawing such as in a good chunk of Canada whereas some soils near or above the Arctic circle dont melt over spans of years.
as for thawing at depth while the surface remains frozen: North hit on that somewhat obliquely. If the avg surface temperature is -10 degC on a scale of weeks/months, then even a very low geothermal gradient would cause the rock to exceed the melting point of ice at roughly 0.5 km depth (that's a very conservative depth; real depth would probably be shallower).