This might be good advice, but it's terrible that we live in a country where this is good advice.
Actually, it would be terrible to live in an environment where it was not good advice.
After all, its good advice if and only if you have some confidence that deadly force will not be used if you cooperate, otherwise, the advice to cooperate when a gun is drawn is bad advice. Otherwise, you should only superficially cooperate while actively looking for an opportunity to overpower or escape (neither of which has a good probability if the attacker has a gun already drawn, but if you don't expect cooperation to be effective protection, you've got no good options.)
Now, it might be terrible live in a place where it is not less likely than it is to be useful advice -- because where we live now, the circumstances in which people might need the advice come up more often than they should. But it would be good advice (with the caveat above) even if it were less frequently needed.
In America, we are so used to violent interaction with authority that most cannot imagine it working any other way.
One of the first steps we should adopt in the US is the mandatory changing of police uniform color. Green or light blue uniforms are less menacing than the typical US all black uniform. I believe this simple change would reduce police violence.
If you google "uk police subdue knife", you can find many examples. Here's one: http://www.huffingtonpost.com/entry/london-police-knife-wiel...
Quote from the article: "In San Francisco, the suspect died in a hail of bullets. In London, the suspect was subdued."
Different situations, different people, I'm sure they're not directly comparable. But in general people are not expected to die from police action in Europe unless they're actively shooting at police officers or hostages or something similar.