This is at least partly false. First, you need to be Mirandized before being interviewed. You do not need to be Mirandized at the moment you are being arrested.
“The Miranda warning (from the U.S. Supreme Court's Miranda v. Arizona decision), requires that officers let you know of certain facts after your arrest, before questioning you.”
Second, you can be arrested with reasonable suspicion even if no charges are ultimately brought;
“In the U.S. and its territories, FBI special agents may make arrests for any federal offense committed in their presence or when they have reasonable grounds to believe that the person to be arrested has committed, or is committing, a felony violation of U.S. laws”
Third, you can be legally arrested by plainclothes officers that identify themselves as police. In some jurisdictions you can even be arrested by another citizen.