A tough one to answer definitively. Technically the picture is stretched on ALL DVD players if it was done properly. The DVD player itself will letterbox the image as it comes out of the player. This is a setting in the DVD player. Typically the factory default is set to 4:3 letterbox meaning that the DVD player is connected to a 4:3 (standard) television set and any 16:9 content should be letterboxed by the DVD player for proper display. The other common setting is 16:9 widescreen meaning that the DVD player is connected to a 16:9 monitor and the output will not be altered coming out of the DVD player…the TV will display in the full 16:9 aspect properly. The thrid setting is 4:3 pan and scan which is really not used to my knowledge and should not be used.
So my theory is that you made the DVD corectly but that DVD player is not set up properly in that it thinks it is connected to a 16:9 widescreen monitor and is not automatically letterboxing the image. I would suggest going through the setup menu in your DVD player and make sure it is set to 4:3 letterbox.
A side note: The easiest and quickest way to figure out if your DVD is properly authored for 16:9 is to put it in a computer DVD player and watch it through the software player NOT full screen. The window should display as a correctly proportioned 16:9 window….not 4:3 letterbox and not 4:3 stretched.
-Matt