Like how come RR and Boeing apparently have no data supporting the theory?
I wouldn't read too much into the lack of response from Boeing or RR. During an accident investigation, the manufactures are effectively under a gag order. All official communications are to come from the investigating agency.
While I've never known an investigating agency to blatantly lie, I have stewed quietly a few times when they couldn't be bothered to officially dismiss speculation or theories that we'd already disproved. All that being said, I think the idea that a US intelligence agency has access to some data that no one else does is plausible, perhaps even likely.
BTW, most modern FDR are capable of recording the max capable flight length, so there is little risk of the relevant data being overwritten unless the plane landed somewhere, refueled, and took off again (at this point I'm not sure I'd rule out much of anything).
The voice recorder is a different story though.