While that may contribute to the slipperiness of ice in certain circumstances, we know that ice is still slippery even when the compressive force is unable to melt the ice, even a thin layer. For example, we've studied ice at temperatures and pressures where liquid water doesn't form.

https://www.youtube.com/watch?v=20zyW0qoSTE

I don't remember the details exactly, but in the (most common) crystalline arrangements of H20, at the surface/edge of ice the individual molecules don't have all their crystalline "partners", so they can still shift around to varying degrees, which makes ice slippery even when none of it can / does melt--all of the molecules are part of at least one crystal.