The right to silence is there so people don't have to incriminate themselves. The question of innocence doesn't come into it.
It is impossible for an innocent person telling the whole truth to incriminate themselves.
Truthful statements by an innocent person[edit]
An incriminating statement includes any statement that tends to increase the danger that the person making the statement will be accused, charged or prosecuted – even if the statement is true, and even if the person is innocent of any crime. Thus, even a person who is innocent of any crime who testifies truthfully can be incriminated by that testimony. The United States Supreme Court has stated that the Fifth Amendment privilege:
protects the innocent as well as the guilty.... one of the Fifth Amendment’s basic functions . . . is to protect innocent men . . . who otherwise might be ensnared by ambiguous circumstances..... truthful responses of an innocent witness, as well as those of a wrongdoer, may provide the government with incriminating evidence from the speaker’s own mouth.[12]
The U.S. Supreme Court has also stated:
Too many, even those who should be better advised, view this privilege as a shelter for wrongdoers. They too readily assume that those who invoke it are either guilty of crime or commit perjury in claiming the privilege.[13]
https://en.wikipedia.org/wiki/Self-incrimination