People tend to forget just how violent martial arts really are. It is quite literally impossible to train without a certain measure of compliance. Even agreeing to release a lock or choke upon your partner's tap, or controlling your striking power, is being compliant to the understanding of having a safe training environment. So there truly is no such thing as a fully non-compliant training.
When someone makes the critique on a particular martial arts video that the partner is being compliant, they often mean they are simply letting it happen. During an instructional demonstration or video, the partner should be letting it happen. Do you have any idea how disrespectful it would be for someone to be teaching a particular technique at half speed with zero power, and the partner just pulls away or starts fighting back? Not only would you be met with a request to leave, you should expect a physical response. A friend of mine once told his demonstration partners, "You can either make me look good, or I will make me look good, and that's going to hurt a lot more." But instructional videos and demonstrations aside, let's look at the role compliance plays in training.