These cokments having nothing to do with going from an HD TV to an old TV.
Old TVs do not have HDCP and will not work with HDCP digital content.
There is a handshake involved. The cable box asks the HDCP TV "are you a recording device". The TV says "no, I'm a TV" and he broadcast plays.
Using an adapter to convert from digital to analog signals will mean that when the cable box asks "are you a recording device?" The adapter and old TV can't answer the question because they are not HDCP, and the broadcast is halted.