But the deck of an oil rig is well above the sea so you would have to add the sight distance from the rig to the horizon.
Excellent point. But the math doesn't help the oil worker's case.
Running the computations for an oil rig platform 100 m above the ocean, and an object 348 Km away at 38,000 ft MSL, the line of sight would be 0.33 deg above the horizontal line of sight. At 100 m elevation, the horizon is 0.32 deg below horizontal. So the object would appear to be approximately 0.65 deg above the visible horizon - slightly more than the width of a full moon.
Certainly on a perfectly clear night you can see the moon rising, so it's obvious that you might be able to see that far. But it requires perfectly clear conditions nearly down to the horizon for 348 km - not common. And the airplane clearly wouldn't appear so high in the sky as to be obviously an airplane - not on a dark nearly moonless night in the middle of the ocean with no visible horizon and thus no clear reference for where the water ended and sky began.
(According to some atmospherics pages, refraction will affect these numbers, but it's hard to predict and may actually be either a positive or negative effect, meaning the farthest visible horizon can appear closer or farther, depending on the temperature gradients in the atmosphere.)
I also must question the oil rig worker's assertion that he could tell the plane was in one piece, and that it wasn't changing aspect and thus going towards or away from him. The best human eye can resolve a 30cm object at 1km; at 348 km this translates to about 100 m. The airplane would thus be slightly below the resolvable size to the human eye with perfect vision - possibly visible but only as an unresolved dot. Any aspect change would be far to slow to be detectable, and any debris cloud or fireball would appear as a single object no matter how segmented.
It would be far more likely that this oil rig worker saw a light flaring from a fairly close ship at that low elevation, than an airplane at 38,000 ft 348 miles away. Both would be at approximately the same location in his field of view. On the other hand, if he saw anything high enough in the sky to be certain it was an airplane instead of a ship, it was far closer than this flight would have been, based on other "known" data.
I'm sure he's not misleading anyone intentionally, but it doesn't pass the math sniff test.
Dip of the Horizon
Visual acuity - Wikipedia, the free encyclopedia