I have the opposite question to one that was asked a little earlier. I have some video that was shot in 16:9, and I need to incorporate it with 4:3 video. I asked someone what I should do, and he suggested that I say "no" when FCP asks to change the settings, and that it would be OK, but I'm still getting a little of the black bars on the top and bottom of the picture. The video is for DVD.
Assuming that your 16:9 footage is also SD (if it's HD, you might be able to drop it into a 4:3 sequence and resize accordingly such that you can get a full-screen center crop going without losing resolution)...
If you drop an anamorphic 16:9 SD clip into a 4:3 sequence, you will get the letterbox. It's got to do with how the pixel aspect ratio allows you to shoot 16:9 SD footage.
If you want the 16:9 footage to fill up the 4:3 screen, you'll need to blow up the footage by increasing the size. But this means you'll lose resolution/quality.
Since you're going to DVD, why don't you continue working on a 16:9 anamorphic sequence, output to compressor & author through DVD Studio Pro. You'll be able to burn a DVD that'll fill the screen on a widescreen TV or automatically letterbox itself on a 4:3 TV.