It depends on what you mean by quality and what they mean by quality.

Pretend you're an asshat lawyer arguing the validity of their statement. All electrical signals are analog. Binary digital signals are both. They happen to encode digital data using a +/-nV square wave. Technically, that's still a type of analog signal.

The receiver buffer is designed with a certain electrical tolerance. Say your standard signal encodings were 0V and +5V. You might design a buffer that will tolerate 0+/-1V and 5+/-1V. Stuff like this is really important in battery powered devices where your input voltage is unknown. Also, the "square wave" produced by the transmit is not a perfect square wave. Looser tolerance on the receive side means the transmit side doesn't have to be as complex or robust (pronounced: expensive to manufacture).

A better cable will obviously make a difference in the electrical signal quality. It might be marginal. You might need very expensive electrical testing equipment to determine it. It certainly won't make a difference in picture quality. Once the electrical signal quality is "good enough" than the the signal is digitally lossless. But electrically, the analog signal carried by the cable is still transmitted "better."

Also,

You can't really improve the signal quality beyond "works or doesn't work".

Yes you can. It's called error rate.