Wide angle lenses are used on many Low Earth Orbit spacecraft, rovers on Mars, etc. in order to fit more visual information into the frame.

If that's a major sticking point for them then you can show images from the Apollo missions, etc. You can even look up what cameras and lenses were used. If they don't think we went to the Moon, show them images from the Lunar Reconnaissance Orbiter of the Apollo landing sites and rover tracks.

But in all probability, your buddy doesn't really care about space, the shape of the planet, history, science, camera specifics, or anything to do with understanding nature for it's own sake. They probably just want to FEEL superior through special or hidden knowledge. As far as I know there's no remedy for that besides some form of ego death.