Ok, let's have one last try to make this really simple.
These recorders just record the video frame they get from the input source. They don't know anything about the intended aspect ratio. They don't know if it's wide-screen 16:9 or 4:3, they don't know if it's letterboxed or pan&scan - that's all up to the source. That input frame will be recorded at 720 x 480 resolution, assuming SP quality or better is selected.
The only way that any DVD player knows what the aspect ratio of a recording "should" be on playback is the aspect ratio field in the title header, i.e., the IFO file on the DVD. DVD recorders do not set that field, so it just defaults to 4:3 (yes, there are some models that provide an option to set it manually, but the Phillips/Magnavox units don't).
DVD players use that aspect ratio field in combination with the "TV type" playback setting (16:9 wide screen, 4:3 letterbox, or 4:3 pan&scan) to decide how to display the recording on your TV. If the aspect ratio field says that the title is wider than your TV, it will add letterboxing above and below - unless you have selected 4:3 pan&scan, in which case it will cut off the edges instead. This is a playback mode setting - these settings exist on all players and recorders, and do not affect recording in any way.
The actual picture you get on your TV on playback will depend on both the DVD player's output, and the use of Zoom and Aspect Ratio controls on the TV and/or the DVD player to modify the picture. You can modify the appearance manually to be correct, even if the aspect ratio field is incorrectly set for the recording.
The best way to record and play back 16:9 wide-screen HDTV broadcasts is:
1. On recording make sure your source is giving you full frame (i.e., "anamorphic") input with no letterboxing, no edges cut off.
2. On playback, set the TV type to 16:9 wide screen
3. On your TV, set the aspect ratio to "Full" or "Stretch", whichever correctly expands the picture to exactly fill the 16:9 screen