It depends on the DVD Recorder.
Over ten years ago, I had a DVD Recorder that could copy copyright-protected tapes and such, however the machine would automatically distort the picture as a result: for instance, after the transfer, the copied video would look like a 240p YouTube video, not to mention the top third of the picture would have a yellowish tint (if some of you are able to remember waaaay back when I first started uploading YouTube videos in 2007 and 2008 before reuploading many of them).
My current DVD Recorder (a Sanyo, which was previously Magnavox), it really depends on the tape: some tapes can be copied, others can't. On the plus side, however, tapes that can be copied can be up-converted to 1080p: it's not perfect, and it enhances artifacts and imperfections, but the quality distortion is minimal.