How? You failed to explain your conclusion with any laws, examples or facts. You just made a general and vague comment that basically equates you your standard, "Not necessarily."
If you are not a suspect in a crime, then the interaction is considered voluntary. Unless you are detained, you are always free to leave and answer no questions.
If you are being detained as part of an investigation, the only thing the law requires is that you identify yourself, which can be done nonverbally by showing ID. While that can be called answering the question "What's your name," you are not making any statements that may be used against you.
if you are under arrest, then you are protected by the 5th amendment, and the "right to remain silent" spelled out in the Miranda warning means just that. They can't get you in trouble for exercising your rights.
Cops try to get everyone to identify themselves "for their report," but it's also an attempt to do a search on your info to check for wants, warrants, etc. If you have the right to not answer any questions, then even "basic" answers should be avoided.
Of course, if you are the victim, then talking to the police is a requirement. Hard to make a complaint without giving details -- that is, if you are interested in getting their help.
I said not necessarily because there are a million different things that can occur in an interraction between cops and the public and small details can make a difference. I would have to write you a whole book to lay out everything.
Let me give you an example where not identifying yourself could make things worse.
Scenario: Officers are looking for Kimo because they have a warrant to arrest him on. Officers see you and you look just like Kimo, same height, weight, and match the most recent photo so they stop you. They ask for your name, date of birth, basic stuff like that but you refuse to provide any information at all. The cops could arrest you for the warrant and be justified legally speaking for making a good faith effort. Eventually your finger prints would be taken and it could be verified that you weren't actually Kimo and you would be released with no charges. Quite the unnecessary inconvenience for you.
The reason that Grovler's advice is poor is because it is a blanket statement to never say anything to cops. If he had said something more specific, like don't answer cops questions about a crime you might be accused of, then that would be sound legal advice.
Refusing to answer even the most basic question, say for example "did you see who robbed that guy?" would raise the cops suspicion and give them some additional reason to dig further.
You are right, that cops will always try to get more information, it serves many different purposes. Not just as a victim or a suspect but also as a witness.