I’m not sure, but I would imagine the JVC hm-dt100u and others might be able to. I could never rely on VCR’s to maintain proper time. As there are so many cable providers, I can’t speak to their capabilities or lack there of. The use of an external tv tuner might be able resuscitate older VCR’s.
VCR in the HDTV era
Can either the auto clock or auto channel set functions of a VCR work in the HDTV era? I'm wondering if cable has any sort of backdrop signal that that VCR can use.