The problem isn't usually going to be that LE is looking to pin a Murder charge on you or looking to get you to say something incriminating with no cause. The problem is that you have just undergone a traumatic experience and your mind is racing with a million thoughts and you might say something that can be misconstrued and come back and haunt you later. Having a lawyer present can stop you from saying this or he can correct or clarify on the spot. He can hear these problems on the spot whereas you may not realize that wasn't exactly what you wanted to say until too late.

It used to be that when LEOs were involved in a shooting they wanted a statement as soon as possible while it was fresh on your mind. Now they recommend at least one good sleep cycle in order for things to have been processed in your mind. A smart officer, or person, consults with his lawyer and writes out a statement that his lawyer has read regarding the incident and presents this to the investigators. If they have any further questions as it regards to the criminal matter, they know to go through the lawyer. The protocol is different for police involved shootings as it pertains to the administrative side of the investigation.