From the article:
Just because you haven’t been read your Miranda Rights doesn’t mean what you say is inadmissible.
I was told by local PD (friendlies) that often they won't read a suspect their rights, but they also won't ask them any questions. If they don't ask, rights don't have to be read yet, and suspects often suffer from diarrhea of the mouth, telling everything before they've even been asked. Whatever you say before you're asked is absolutely given of your own free will and perfectly admissible.
It's a bit more complex than that. The officer can ask any questions they want before reading someone their rights... they just can't ask questions after the person has been detained (without reading Miranda Rights)
So if an officer walks up to you and says, "Good morning, what is going on here?" and you say, "I just stabbed someone 7 times in the alley over there" and the officer says, "that's it, you're under arrested" you can't say, "haha, gottcha... you didn't read me my Miranda Rights, and can't use that in court".
Technically, the officer never said, "stop, you're being detained. Tell me that's going on here". You always had the opportunity to not answer the officer and to walk away when s/he asked what is going on.
Those two might not sound very different, but they are extremely different in a court of law.
It's not until you say something along the lines of, "I'm going to leave" and the officer says, "no you're not, you're under arrest" that they have to read you your rights. (or, if they've cuffed you and physically detained you)
EDIT: Crap, Endurance already said pretty much exactly the same thing