It's a property of the DVD, when the company making the DVD has chosen to use the Macrovision copy-protection mechanism. The DVD Player/Recorder is innocent, and will have no effect on that mechanism.
Sounds like, since your VCR is integrated with the TV, and you apparently can't get around the VCR, you need one of those Macrovision-defeating boxes that are easily obtained at most consumer electronics stores.
More involved and questionably-legal approaches involve ripping the DVD to another that removes the Macrovision copy protection. But we tend not to talk about such things around here.