He'd learnt it on a ship he'd sailed on in the late 50s-early 60s. Is this the 'folk process' at work?

Yes, it is. Maybe I was wrong about ye old Rambler!

On the other hand, I remember at one time it was quite the thing for kids to sing "Georgie Best, superstar" (those of us of a certain age will recall the next line, although precisely why it attached itself to Mr Best I've never known) - and I'm sure not all of them knew that they were singing a variant on "Jesus Christ Superstar". Does that make "JCS" a folk song? I don't really think so.

There's quite a useful word for the kind of thing we're talking about, viz. filk (although the filkers themselves, rather annoyingly, define filk as if they invented it). The activity of filksinging - writing new songs that piggyback on old ones - is a form of folksong, but I don't think the resulting songs are folk songs, because they aren't independent enough of the original source. But it's an interesting one (where by 'interesting' I mean 'I'm not sure what I think about it').