Occasionally I see a paper train reproduction during the York Meet; once in a while, an original. An original is die-cut: parts are pushed out along perforations. As far as I know, reproductions have to be cut out and assembled, as you mentioned.
Breakfast cereal companies offered lots of push-out paper premiums, and this paper train was among them. It was approved by Lionel, but it was made by a company that specialized in such products. Some of these were printed on the backs of cereal boxes.