All the details aside, there is no RNAV system certified that won't
handle both flyby and flyover waypoints.

Such a limited system could not fly any GPS approaches, because they all
have a flyover waypoint to begin the missed approach.

So, you were being fed some kind of BS.

Also, as to Part 135 single-engine contingencies, they could have a
different procedure than the ODP for Runway 8, if their company chose to.

I will check out the Primus 1000 with some pilots that fly that system. ;-)