"Sir, do you know how fast you were going?"
Presumably both "yes" and "no" would be bad. (The former is obvious, and the latter could mean you're not paying sufficient attention, etc.) So, do you just stare at them in silence? Do you say something like, "I'd rather not answer," which while accurate, sure sounds like "yes". (At the very least, there goes your chance of a warning instead of a ticket...)[1]
I agree with serve_yay that many of these situations start off seeming innocuous, and staying silent is easier said than done.
Another example is the cops canvasing the area of a crime, looking for info. Do you just refuse to speak to them without a lawyer, even though you had nothing to do with it? It's certainly possible (albeit unlikely) that they actually have you as a suspect and are trying to trick you into some sort of false statement. (Or a statement that appears to be false because it conflicts with other evidence, even if it's true!) But in the vast majority of cases it'll be exactly what it seems. Or say you actually witnessed a crime. Or were the victim! Still lawyer up before talking to the cops? It appears the safest thing is, yes, always get a lawyer. But at some point on the spectrum, does the cost and inconvenience outweigh the insurance factor of doing so?
[1] I've only been in that situation a couple times, but I've tried my best to answer politely without saying anything material. One way to do that is to answer questions with questions. "Do you know how fast you were going?" "How fast was I going, Sir?"