For an extremely cynical viewpoint... why wouldn't you? You're police. Your word is automatically considered more reliable than a civilian's and in direct dispute, you win by default. The only check and balance against you... is your own department that's more worried about public appearance than getting things done. And even if some dirt comes up against you, you can pull out the "we serve the people and put ourselves in harms way for you" card to guilt trip people into trusting you.

If I was a characterless person... I'd lie every chance too. You've got such a high success rate.