If you want to compare it with a breathalyzer -- the reason we put trust in the breathalyzer is that we know there is a physical cause (amount of alcohol in the blood) that we are trying to measure. In the polygraph case, we are trying to measure 'level of lying', which is not physical in the same sense. For your argumentation to make sense, you would need to propose something like a 'lie particle' that is emitted by people that lie. Come to think of it, this is really very close to what proponents of polygraphy argue!
What is needed (as a sufficient condition), is the ability to compete. Without competition, no free market. However, property rights are not sufficient for competition. If I own the widget market, and have a gaziilion bucks, I can stop competition. How I will do that? Well, when you with your meagre million start to create and sell widgets, I will undercut you. I will sell at a loss. I will give it away for free. I will give it away for free until you are broke. I've got a gazillion bucks, I can give it away for free for a very long time. Then I (or my offspring) will raise prices again, and will get the rest of my gazillion dollars back. If you also have a gazillion dollars, we will meet and agree not to harass each other. We will also agree to help each other to keep everyone else out. We both have a gazillion, and if we do this, we will each have 2 gazillion, instead of each having only having 1 gazillion due to us competing. Because it is just us two, or maybe a handful, we can do this, using promises we give in person. Promises we will keep because it will make each of us richer. We will still dictate price to a level that optimizes our income.
So, who can make sure that I do not give away my produce for free to kill all competition? Who can make sure that I'm not determining price with my competitors? The free market? You've got to be kidding. There's only one entity that can do this: the law, i.e., government. It is a job for government to keep the free market competitive and to limit the negative effects of excess capital. Read that again: negative effects of excess capital. The government needs to keep the market competitive for it to remain free. If you don't believe me, please explain how the scenario's I sketched above are countered by property rights alone. We need a right to compete for it to work.