Fully exerting your rights might be a little antagonistic in this situation but you may also wish to give a complete non-answer, like "Yes, but I'm sure you're going to tell me."
Even if you just think you're just a witness to a crime, they might think otherwise. I'd tell people to trust their judgment but prisons are filled with people who trusted their judgment and thought that talking was OK, so clearly that's not always enough.
There's a great point/counter point of the issue from a law school class. It's a bit long, but well worth a watch:
In the criminal sphere, the motto (slogan, who knows what real strength it has, these days) "Innocent until proven guilty" was presented and meant by at least some as a counter-balance to such demands. Presumption of innocence was... well, at least "presumed" to mean that the system would work on your behalf towards an accurate resolution rather than just a convenient one.
Contrary to this, however, note that a validated and often employed legal strategy is to simply spend the opposing party into defeat. (Or, threaten to do so.) This happens in the civil arena. It also happens in the criminal arena, where the State can choose to bring relatively unlimited resources to bear against an individual opponent. (We are, as the general public, increasingly learning just how little oversight and restraint is exercised in how this is employed.)
They may not have to "prove" anything. Employing a litany of court dates, expert witnesses, appeals, etc., they can simply "run out the clock" of their opponent's financial resources (to mix my metaphors). Further, in the criminal sphere, we continue to learn more and to read and hear about just how far off the rails surveillance, unwarranted search, entrapment, interrogation, etc. can go.
Then, we also have the increasing use of forfeiture to peremptorily seize resources with no opportunity for defense. The increasingly broad and inappropriate use of no-knock search warrants that physically threaten well-being. Swat-ification that is turning policing into militarized occupation and further separating the police from the community...
Whose fault is this? Probably all of ours. Regardless, it is turning the legal system, for the general public, from something to respect to something to fear. It is not "our system", anymore, but "theirs". For various values of "theirs".
Not a good recipe for a society "based upon law".
P.S. I should add that I recognize what others say, that the U.S. is still comparatively quite good compared to many other places in the world.
But I worry about the delta. As well as persistent... "outliers" than do not seem to improve nor resolve. And than may be far more extensive than we, the "general public", were once led to believe.
If you see some old lady get robbed, that's not coming back on you.
Also, if the police don't put you under custody, you don't get Miranda rights and you don't get the right to a lawyer necessarily. You'd have to pay one yourself.
Unfortunately, "just use a little sense" may be dangerous advice. Here's a story from earlier this year about a guy who called 911 when he came across an injured person lying in the street. As thanks for his trouble, he was assaulted by police, arrested, and spent twelve hours in jail -- mostly in solitary confinement: https://news.ycombinator.com/item?id=7233730
I think most people either don't realize or choose to ignore the fact that calling the police rarely prevents any crime. It can be effective if what you're seeking is retribution or revenge, but once you've been stabbed whether you heal or not doesn't really depend on whether you answer questions from the police.
The news from Ferguson is a reminder that bringing police into a situation can make many situations much worse for everyone. If I find you bleeding in the street I'll help you get medical care and if you want to go to the police that's your decision, not mine.
This is a somewhat absurd argument because what I'd do ultimately depends on the circumstance. If I truly know nothing besides my own name and that I found this person bleeding, I would be wondering where my other memories went and if I were brain damaged.
In the general case, they aren't going to be sending detectives immediately to ask questions because someone called 911. Nor would I stay on the scene longer than I was medically needed to be there. But the "general case" is a useless fiction.
As far as I know this applies for all questioning, regardless of whether you're free to go, being detained, or under arrest. IANAL but I've had plenty of encounters with police.
The key right you're asserting is not a "right to a lawyer" it's the right to remain silent. Asking for a lawyer helps you to do this, because otherwise they have much more latitude to try to convince or trick you into talking. If you said you are remaining silent until you talk to a lawyer, in theory, they have to leave you alone until the lawyer is there.
If you aren't in custody, they don't have to provide an attorney and they can keep asking questions.
And custody can be fairly broad, for example a traffic stop doesn't count.
I am not advocating getting a lawyer if you are a witness to a crime. Simply if they have it in their minds you have done something wrong politely tell them you will gladly answer all of their questions once you have proper legal counsel. An no this advice doesn't apply to mundane things like speeding tickets and the like.