3 way connection without 3 way switch
I think you may be mistaken about what the wires are. Since it's not a "smart" switch, there's likely not a neutral connected to it.  Instead, I would suspect that the white wire is actually being used as a traveler. This was a fairly common wiring method, before the neutral was required at all switch locations.



If this is the case, then you should mark the white wire at both ends with a black marker or tape.  This would also mean that you're not going to be able to install the "smart" switch, as there's not a neutral in the box.

Remember, not all neutrals are white, and not all white wires are neutral.

I'm no good at ASCII art, so here's a crappy MSPaint digram of what the wiring might look like.