This handy calculator will allow everyone to experiment with the likely visual horizon for two points of any altitude:
Horizon calculator - radar and visual
If you use 35K for the aircraft and say 150ft for the rig worker then the horizon is at 244 miles...
Unfortunately, even allowing for some distance covered, at 370 miles away there's just NO WAY this rig worker saw the aircraft... it was something else. My bet is on a meteorite. Just another case of putting 2 and 2 together and getting 5.