https://torontosun.com/news/local-news/warmington-top-cop-wa...
https://torontosun.com/news/local-news/warmington-top-cop-wa...
The implication that "the police say this because they can't stop the crime" is IMO not the right take-away. The correct take-away is that a certain level of crime is unavoidable in practice, and you should prioritize your life over your property.
With breaking and entering, the goal is to get what they can with a minimum of fuss. Locked doors, barking dogs, automatic lights, security systems, etc are all great deterrents, because the goal is to get as much as possible while avoiding capture. The table stakes are that the burglar can get in and out without getting caught.
With home invasion, the whole threat profile is different. The operating premise is that the invader will use violence or the threat of it to brutalize the home occupants into facilitating the theft, the escape, and avoidance of prosecution.
Think of how wild animals engage in violence: they will not enter into a violent situation unless trapped (either physically, or by circumstance - e.g. fight or starve), or they think they can win the fight without sustaining any substantial injury. In the case of a home invasion, you are trapped, but the other guy has chosen the fight.
All of that to say, compliance should be done in the light of keeping yourself and those around you together and unharmed, and not willy-nilly. Obviously, don't pick a fight over a TV. But understand that if they continue their breaking-and-entering after they know you're there, compliance may be insufficient to protect your life.
The term comes from tenants breaking the boarded up door and entering their own home.