Frankly, you've allowed yourself to fall prey to US election year propaganda. If you look at the numbers you're very safe travelling in the US, and to the extent you're in danger it's from criminals and not police.
0: https://www.youtube.com/watch?v=6wXkI4t7nuc
1: https://www.youtube.com/watch?v=UezKO4TnaHs
That's simply false. In criminal matters you have exactly the same rights as a US citizen, even if you're in the country illegally. Though it is true you don't want to say anything to cops if they've taken some kind of official notice of you, that's not the same thing as asking for directions or reporting a crime.
You will get the same advice about answering questions in Canada, by the way, and for the same reason:
>Never voluntarily subject yourself to a police interrogation where it is apparent you are a suspect or accused. If you are approached as a witness you can ask the police, on videotape, to confirm that you are being questioned only as a witness and that you are not in legal jeopardy. After an arrest, there is an enormous power imbalance. The police -- hopeful of obtaining a confession, or damaging admission -- will take advantage of your vulnerability, at least to the limits of the law. Your best choice is always to consult a lawyer and you have a right to free consultation with duty counsel.
http://www.cbc.ca/thenational/blog/2012/06/what-to-do-when-t...
The reason people hammer home the idea you shouldn't talk to cops in the US is (like Canada) remaining silent isn't prejudicial during a trial. You have nothing to gain and can only hurt yourself.
In practice? Enjoy jail and a swift deportation because you happened to say the wrong thing to an officer or otherwise incur their disgust. What an embarrassing, and costly, end to a business trip that would be.
It should be common sense you don't go to a foreign country and break the laws, no matter where you're from or where you're going.
Did you even read the original article?