I don't even understand the pitch? you have the disc playing, in your hands, your ownership, no buffering, no subscription required. and they're saying....hey do you want a worse experience?
Proof? There are other (some equally creepy) ways that it could get this info. Depending upon how the DVD player is connected, it could simply be getting info from that. It could also be taking occasional screenshots. There are other things as well.
Edit: poster below links to Roku and they use screenshots.