Massive stars need not necessarily be in the *red* supergiant phase at the moment of core collapse. Such stars--if of sufficient mass--are believed to re-cross the Cepheid instability strip a couple or more times. The core could conceivably collapse at most any stage of this process.
The presence of the companion may have little impact, at least as far as its 'robbing' of some of the outer envelope of the other star is concerned. The veritable vaccuum of the tenuous envelope has nothing, really, to do with what's going on in the comparatively minute (planet-sized), super-dense core.
The current consensus on Type II supernovae is that the progenitor stars are either RSG's or blue giants. Back in the 1980's and earlier, it was only thought that RSG's would go supernova (it was a great shock when the progenitor for SN 1987A was found to be a ~20-25 M_sun blue star!). While massive stars can cross the instability strip multiple times during their lives, it is usually thought that they will end it at one extreme or the other of the loops they trace on the HR diagram, as the the time spent on each loop is very short compared to the life of the star. Hence the necessity of arguing that this particular star was, in fact, a YSG.
According to the current understanding, the progenitor of SN 2011dh should have been a RSG when it blew up, as it was not massive enough to blow off its envelope and return to being a blue supergiant. This seems to be the motivation for introducing a companion which was stripping mass from the star and allowing it to remain yellow.