Well, simply passing the image through the recorder it would know to record the anamorphic flag on the disc, but it wouldn't be able to modify the image since it isn't going through the MPEG2 decoder (you're just seeing the raw analog signal). But once it's on disc and playing it back, it sees the flag and the decoder knows exactly how to format the video.

Now as you say it's being erratic and jumping between different modes... this is very odd. Let me know how a VCR behaves. This is either something odd about the R15's output, or something odd about the way the DVDR is recording it (since it doesn't flash back and forth playing back commercial DVDs).