Someone with one functioning eye cannot see stereoscopically, by definition. They can, however, make up for the lack of stereoscopic depth perception by using various visual cues and experience.
Where there is little ancillary information to help in depth perception, say flying a helicopter over the North Sea at night, it might be expected that someone without stereoscopic depth perception may have more difficulty.
I don't think the CAA are unreasonable to want to investigate this. I think they are unreasonable if they help someone with a licence to keep it, but at the same time refuse a certificate to someone without a licence.
QDM