The Miranda decision resulted from an attempt to stop coercive questioning -- including physical force, btw. Even without intending to, police questioning is frequently coercive before of the power situation. But Chicago has just been caught short for rubber hose use, and questioning that goes on for hours is still common place. MIRANDA is an attempt to balance out the power issue.
But your example is what is known as a spontaneous statement. It's been freely volunteered and did not result from any questioning. So it's an exception to the Miranda rule and both your statement and all evidence stemming from it could be used at trial.
There are gray areas. Big, big gray areas. There was a case few years back where the police had a suspect in the back of a car, taking him to the station. They didn't ask him any questions, but instead talked among themselves about how cold it was out, and how the body of the murder victim (a child iirc) was lying in the dark, and how his family was grieving.
The suspect told the cops where to find the body. The question was, was that a form of questioning. Trickery, to be sure, intended to get him to confess, but was it allowable under Miranda?
I think the courts (maybe even the SCOTUS) ruled that it was, but I can't for the life of me remember for sure. Perhaps someone can enlighten me. I remember the case, but we don't use it in New Hampshire. (NH's Constitution is better in this area then the Federal Constitution so we rely on cases within the State for this issue.) I think it was allowed.
One case involving the police putting a colander of the suspect's head and running a piece of string to a copying machine. When the button on the copying machine was pressed, the word "LIAR!" came popping out. Guy thought he was connected to a lie detector machine and eventually confessed. If I remember right, the trial court allowed it, but it was eventually thrown out.
Police are a lot smarter and are creative. Criminals, especially career criminals, are not. Again, the courts are trying to even the playing field a bit.
But you need to understand that if you're in a small room, being questioned for hours, your desire to fit in and cooperate will likely kick in. People have confessed to things they haven't done as a result.