All we have so far is - "According to a CAB specialist the American Legacy pilot said, during the post-accident debrief, that he'd decided to climb from FL370 to FL390 to gain speed and range, without informing ATC, and that he'd switched off the transponder (for reasons unknown)".
None of this makes any sense. Neither the act - or the (seemingly immediate) admission. If a guy is capable of making himself deliberately TCAS invisible in order to stretch a few miles extra range then he's more than capable of lying to cover his tracks when found out.
............without informing ATC, and that he'd switched off the transponder (for reasons unknown)".
I smell mucho rats here.