It's really an issue of low-level buoyancy. If you can get enough low-level buoyancy, that aids (or at least doesn't act as a deterrent) in the vertical stretching of near surface vorticity, then you are golden. Likewise, weaker low-level laps rates equates to less low level acceleration and makes it harder to stretch near surface vorticity.
So there may not necessarily be a CAP (there could be no CIN), but it's still hard to punch through the layer with very weak buoyancy.
It is possible for low-level dynamics to overcome this issue, but we don't really have a good understanding at this point of which conditions do, and which do not permit this "compensation."
For those of you who are more technically inclined, it's not actually the low level buoyancy that does the near surface stretching. It's actually the buoyancy-driven low pressure that sits at the updraft bottom, and the associated upward accelerations below the updraft base and the center of this low pressure. When low-level buoyancy is stronger, this low pressure feature is also stronger. Note that this effect is separate from the low-level dynamic accelerations driven by rotationally driven low dynamic pressure.