These guys were American pilots.
American/Canadian pilots, and every other pilot on the planet at some point will fly through "Structured" airspace. Which means certain normally reserved eastbound/westbound levels are switched to accomodate heavy traffic flows.
It's up to the Controller to enforce those rules.
Also in the two major non-radar areas I work around, and they are the busiest non-radar areas out there, there is no such thing as a "Wrong-Way level"
For example in Gander Oceanic, and NY Oceanic (Two of the biggest and busiest non-radar areas on the planet) airplanes routinely fly what would normally be considered "WestBound" levels, eastbound and vice versa.
It has to be that way because of the required extra separation required, in order to accomodate the ever growing traffic volume. When they enter radar airspace, we identify them, and put them to a "Right Way" level.
What I'm getting at here is that flying at FL370 westbound would not be as strange to these pilots as some on this board seem to think, in fact if they're in and out of radar airspace, to them it would be routine I've never had a pilot ask me "Hey Center should we really be at this level?"
Let me also add that everyday I get professional pilots, from all the biggest majors in the world asking for an inappropriate level for no reason other than performance, so being a biz-jet and being cleared at a certain flight level, it would never cross their minds, or the minds of most pilots to question the flight level.
My opinion of course, and based on the few facts we have on the subject.