Hmm, maybe some, but I remember when it was released everybody (or very nearly everybody anyway) knew it was by Rodgers and Hammerstein, or at least 'that song from Carousel'. I don't remember any attempt to pass it off as an original?
Indeed we did. Joined in in the North Stand (with my scarf held high) many times in the 1970s. As you say every club used to sing it, in fact some Celtic fans (not a particularly bright lot admittedly), think they started it and Liverpool copied them!