In reply to:
But even if they are letterboxed, shouldn't they fill the screen side to side?
Not if your monitor is set to 4:3 mode. In 4:3 mode for the display you would always have black bars on the sides.
If the DVDs are not anamorphic, then the player is outputting a 4:3 image regardless if you choose fullscreen or widescreen on the DVD.
You are using the widescreen image but the output is still 4:3 (just with black bars on top/bottom). So when you tell your monitor to use 16:9 mode, it stretches this 4:3 widescreen image accross the width of your TV (making it look stretched/wider).
I would agree that it is probably the DVD's themselves. If they are not anamorphic, then they only look right on a 4:3 TV.
Could be your player not interpreting the aspect ratios from the DVD correctly. Take the DVD's to a friends with a different setup (but still a 16:9 display) and see.