In the UK, SubP, the ''fish finger' was made popular around the fifties/sixties, and was an offshoot of the 'fishcake', with the former covered in crumby batter, and the latter mainly potato! It was probably similar to what you were served up...
In fact, only recently, for the first time too, I had some fish fingers which had been in the freezer for a long time, so stripped off the batter and chucked it, just to get at the fish 'finger'. It was tiny, but identifiable as a piece of fish and not mechanically formed, like chicken is dealt with, but the pile of batter was much bigger, so you're probably right that it is a bit of creativity somewhere, but which has made them so popular over here! Kids - and grown-ups usually love 'em!
Birds Eye are actually pretty good with their products here, and their frozen veg are usually superior to 'own-brands', (I suspect that sometimes they're the same thing, but lets not be churlish), and their branding with a bewhiskered naval bloke grinning into the camera has endured for ages! Marketing, eh?
I guess mechanically retrieved fish is probably very difficult as the tiny bones would get mashed as well - maybe they are, but with chicken, turkey etc, it's probably a bit easier...
Enjoy your sarni anyway!