That is really strange, but ... 4 or so years ago I bought another mismatched pipe with a Peterson p-lip stem exactly like that one. It could be that back in the early 20th century, it was recognized that an amber p-lip stem was very desirable, but couldn't be made by anyone other than Peterson, without infringing on the patent - besides, this wasn't an easy thing to create. So people bought a Patent and used the stem for a different maker's pipe?
On the one below, the bone screw in the shank was twice as wide as the piece that was broken off in the amber stem. There is glue residue on the facing of each, so they probably removed the tenon in the stummel, broke off the Peterson tenon coming out of the stem, and glued the two together.
I have been waiting ever since for a stemless 155 Patent bowl to show up!