No defense attorney would advise anyone to make statements to the police and no police would ever advise anyone they have a constitutional right to remain silent, unless they arrest them and read them their Miranda rights.
Especially if one is arrested, they are probably totally out of their environment, they are amateurs among professionals. Every word anybody says can and will be used against them if they are prosecuted.
Every statements anyone makes to the police can be interpreted in a different way that the way they meant it. Every piece of evidence, physical or circumstantial can be also interpreted in different ways.
Remember that although police are professionals and are not out there to "get you" they are humans and like all humans they can make mistakes. The overwhelming majority of conviction are secured by statements made by the defendants themselves and there are plenty of people that have been convicted and subsequently exonerated, and those are only the one we are aware of.
To ask for counsel cannot be construed by a jury as an admission of guilt and one does not need to be guilty to ask for counsel.
Attorneys are the only ones that have a professional duty to defend suspects, no one else does. Remember that the role of the police is to gather evidence and not to establish guilt or innocence, that is for a jury of one's peers to decide.
People are innocent until proven guilty in a court of law and one's right to counsel and/or to remain silent is enshrined in the constitution for very good reasons having to do, among other things, with fairness, justice and liberty.