Well that's something I've heard too - if you are calling about a break in, make sure to mention that you think you saw them carrying a gun/knife. Then they will actually send someone within 5 minutes. Otherwise? They will be gone long before anyone turns up.
And no, I'm not talking about purely hypothetical situation here - my sister was alone at home when two drunk guys were trying to break in, throwing rocks and bricks at the windows, shouting that they are going to come in and get her, she locked herself in her room and rang the police.........they arrived 45 minutes later. If one of the guys didn't cut himself badly on the glass and decided to give up(and the other one bailed then), it could have ended extremely badly, but an active break-in is apparently not enough to send the nearest PC to the scene right now.
And no, I'm not talking about purely hypothetical situation here - my sister was alone at home when two drunk guys were trying to break in, throwing rocks and bricks at the windows, shouting that they are going to come in and get her, she locked herself in her room and rang the police.........they arrived 45 minutes later. If one of the guys didn't cut himself badly on the glass and decided to give up(and the other one bailed then), it could have ended extremely badly, but an active break-in is apparently not enough to send the nearest PC to the scene right now.