Please do not mistake my attempt at explanations as endorsements of the explanation.

The line between comfort and fear is a sentence. So to the first question, sometimes. A date is about feeling out a person, so fear is certainly a part of the equation at times.

Regarding a man being afraid of a date with a woman, probably due to a perpetually-online mindset that false-accusations are commonplace? That's the best I can come up with.

In general, I think you're right to be skeptical, but hype and fear sell. Reasonable rationality does not.