What Heinlein said
This seems like a perfect illustration of "An armed society is a polite society".
As a legally armed, responsible citizen, you not only obeyed the letter of the law, but the spirit of it. In a friendly, polite manner, you not only informed the LEO that you were legally armed, but (implicit in that) that you were fully deserving to be so. Seeing you as an armed, responsible and morally right person (a lawbreaker would not be CCW or polite), he treated you as an equal, or, at least, as one who had earned a greater level of respect than a regular citizen.
Sometimes, I think that saying, "I know my rights!" is the worst thing you can say. First, a lot of people who say it really
don't know their rights, but they don't want to look too easily cowed. Second, a lot of them sound like they are really saying, "You don't have any rights over me!" Third, the people who usually say these things rarely take the opportunity to exercise those rights in the first place, or fight for them, and so exercise them somewhat hypocritically.
You knew the law. You knew what the correct procedures were, and you followed them.
And, whatever your personal feelings toward police officers may be, you treated him with the respect that the uniform, and the position, accords him. And, rightly so, he responded to you in kind.
Bet you didn't realize you were this deep!