You are right. They did show patience by not completely storming his house after two police officers were shot, but, they also escalated the stress an already over-the-edge person was experiencing, and they were not showing patience when they did that. 

The police showing up with a tank, excavator, shouting through a bull-horn, and lobbing gas and stun grenades at him created this situation. A mentally-disturbed person isn't as responsible as are the authorities because he is *mentally-disturbed*. He is not being rational.

Rational, calm, good judgment was in order to prevent the situation from escalating, yet a militarized-looking police force at your door is decidedly threatening. Most people would be able to predict what his response to that would be.