The judiciary cannot force you to prove your innocence. But it can force you to provide evidence, which the state may then be able to use to prove your guilt.
Everybody has a duty to cooperate with litigation. Even third party witnesses who are not "on trial" can be compelled to take testify about what they saw or heard.
Writs subpoena (court orders to testify or produce documents) had been part of the English legal system for almost 400 years at the time the Constitution was written. So when the Framers wrote that no one "shall be compelled in any [1] criminal case [2] to be a witness [3] against himself," that's what they meant. Had they intended to limit courts' subpoena power in civil cases, as to non-testimonial conduct, or as to testimony against other people, they would have said so.
Everybody has a duty to cooperate with litigation. Even third party witnesses who are not "on trial" can be compelled to take testify about what they saw or heard.