I'm pretty sure they shoot innocents a lot less. But I'm in it for the entertainment, not because they follow the law.

Interestingly, in Elementary they call out your issue of always finding probable cause to enter a home. They end up in court over it. It's still basically hand waved off with them asking if they are being called liars and if they have proof. But they aren't even cops, they are consultants, so I'm not sure probable cause even applies. Seems more likely they shouldn't be able to do shit unless they suspicion of imminent danger.