Normally the go-to FE position is that these are generally "fish-eye" lenses that produce a wide range of observable convex and concave curvature as the horizon moves about in the viewfinder. And I agree with that general assessment.
But in the interest of poking around I came across this balloon launching guy/channel. He's recently been doing some interesting launches with multi cams and specifically non-fish-eye lenses. As well, he's added infrared to the arsenal. So have a look for yourself. His second most recent launch is here:
I was frame-by-framing it around the 112,000 ft mark trying the get the horizon right in the middle to limit distortion as much as possible, especially in the lower right infrared view. Interestingly, that view uses a GoPro Hero 4 Black with 7.2mm Lens, spec'd as non-fisheye. Around 1:57;47 you can see this infrared image, lower right.
I'm sure the jury's out, but it's a pretty compelling image.