An open verdict I think.
No - also his children said that they left him with their nurse maid before the fall, in the end - nobody was in the room, which was by the way not the room of Berthier but that of his children - and therefore I would find it odd that those magic agents - disguised Russian officers - would all of a sudden pop up, rush through the palace find that poor Alexandre is in his children's room, throw him out in view of numerous witnesses.
The police - who had up to 5 men to observe the palace - would surley have noted that.
I find it bizare how pure speculation, based on nothing other than speculation of a most unlikley scenario is still regarded as possibility.
Verdict : Waste of my time in the archives and on the spots, it would have been better to claim that spacemen dashed down from the sky and induced poor old Berthier to jump