This is a common misconception for people who get their legal knowledge from TV. You're referring to the Miranda warnings (right to remain silent, anything said can be used against you in court, right to an attorney, & right to have an attorney appointed if you can't afford one). Miranda warnings only need to be given before an arrested person is questioned by police, NOT at the time of arrest. Some police agencies have a policy to read them at time of arrest, but it in no way is mandatory. Additionally, failure to give Miranda warnings does not affect the legality/legitimacy of the arrest, it just means that any statements given by the arrested person in response to police questioning will not be admitted into evidence in court.