By re-evaluating the hard-wall collisionless electron heating model from first principles, we show that despite previous criticisms (Gozadinos et al 2001 Phys. Rev. Lett. 87 [http://dx.doi.org/10.1103/PhysRevLett.87.135004] 135004 ), this model can in general be made consistent with the requirement of radio frequency (rf) current continuity at the sheath edge, while still producing a net heating effect. In addition, we demonstrate that the hard-wall and kinetic-fluid heating models stem from the same basic physical mechanism, and are in many ways the same theory; they differ only in the spatial region where electron heating is assumed to occur, and the way in which the effective electron distribution function is determined. Fundamentally, both models predict that collisionless heating occurs because of a non-isothermal compression and expansion of the plasma electrons by an oscillating rf sheath.