Other than responsible for not seeing a fast moving jet rear-end him, not very responsible. Even if he was under radio control and his head on a swivel, it would have have been near impossible to see the jet coming from behind and left at that speed. He wasn't "near a military airfield" - he had taken off from a general aviation airport just north of Charleston's International airport (CHS), also shared with military, however FAA ATC and rules prevail in this airspace. There is no "military airfield" difference around CHS. The F-16 was on a practice approach to CHS, just as anyone could do a practice approach to CHS by requesting to do so from ATC. One major contributing issue to this was the controller descending the F-16 to such a low altitude so far out (1600' at 34 miles out) [1]. This is well below any slide glope and frankly, as a pilot who flies IFR and no-radio-VFR, I would never expect to see a jet on an approach that low even 15 miles out.
The incident did not occur in the military operation areas (MOA) north of CHS.
[1] http://www.ntsb.gov/_layouts/ntsb.aviation/brief.aspx?ev_id=...