Context is king. What is the context in which the LEO makes that statement?
And it is very correct to say that citizens are not only expected to comply with lawful commands, but they are required by law to do so. This is where the balking against duly constituted authority comes into play.
If the LEO is in an argument with a person and has the legal authority to issue a lawful command to a motorist, say, and the motorist starts arguing and not complying, then a LEOs statement like that is correct. He or she IS the law right there on the side of the highway, i.e. the lawful and duly constituted representative of the law. He or she can do whatever the "law" could do were it a person and able to so.
And while the public is the public, I doubt if the word employer would apply that much. We are not in the strictest sense the employer of the officer. As a motorist stopped on a highway, it is not accurate to say that you are his or her boss, not in the sense in which I think you mean it, i.e. he or she is personally responsible to you for what they are about to do.
They keep the public safe because it is the right thing to do, because they have sworn to uphold the law, and because of the authority they have. Without the authority given to them by us, the people, they could not do their job.
If a LEO is just saying I AM THE LAW as in I Am DA MAN!, that is different.
There are a lot of reasons why LEOS keep the public safe. Number one is it is their sworn duty, not because it is the right thing to do. They joined, most of them, because they wanted to do the right thing, to make a difference in the world.
Keep in mind that for every GG they come across who is just as cooperative as can be, they come across ten folks who are way way above any law known to man. They are truly a law unto themselves, and this is the kind of thing the LEO has to deal with every day. I would not contend for a moment that those kinds of folks are the employers of the LEO. Only in a very very vague way and so vague as to be almost meaningless.
This is why I laugh when I see a motorist on Tv who just got a ticket exclaiming I PAY YOUR SALARY. YOU WORK FOR ME. That is most untrue. Certainly untrue in the sense that the motorist means it. i.e. that the LEO must answer to the motorist for any actions taken. I doubt that the motorist has a chunk of change taken out of his salary that is specifically earmarked for the PD. So as a member of millions of people called The Public, yes, but in a personal sense, the way the motorist would LIKE it to be, nope.
On another note, it is absolutely astounding how restrained LEOS are with the very large lawless segment of the public. I have seen instances where they actually had authority to shoot but witheld fire, so they would not have to kill someone, even though they thereby exposed themselves to risk of being killed.
They don't get enough credit. We don't like them but we pick up the phone and hit 911, not 411.
Keep in mind that there are a lot of people who are their own law. They do not recognize our laws. They have within themselves their very own House of Representatives, Senate, judiciary, executive branches, all in their heads, and they are the ones who decide what they will do and when. There is a very significant number of these people walking around as we speak. LEOS do not know who is who among the public.
When they say they are the law, it depends completely on how they mean that statement. In one sense they are correct, in the other, they are abusing authority.