Side cutting can openers are supposed to split the bead rather more to the top so that the top of the can remains sturdy and the neither top nor bottom have any sharp edges.

I just looked at a can I opened with one yesterday and the can top is sound with nary a sharp edge to be seen. I ran my thumb over both sides and found both sides to be quite smooth. I suppose it isn't impossible that you got a unit that was manufactured poorly. Particularly before they became more common.