belfast, according to this source, SOCAN copyrighted the song, written by Rose Bonne and Alan Mills, in 1952. If it was written the same year as the copyright, then yes, what you've described is a bit "anachronistic".

"And, if it is, am I being incredibly petty for noticing it?"

I don't think so. Certainly not on a serious folk-musician's site like Mudcat, anyway!

I LOVED that song as kid ... :>)   

daylia