Legal rights apply to EVERYONE, regardless of confessions, etc. Legal rights are in place to protect everyone from arbitrary treatment by the state and in evolved societies cannot be be made not to apply to him.
ie. Tsarnaev still has the right to due process, the right not be be subjected to cruel and unusual punishment, the right to representation, etc.
The State cannot take them away arbitrarily just because of whatever condition you feel meets your need for vengenance, because that removes the very essence of what a legal right is - a protection guaranteed by the supreme law of the land.
It is his right to have the evidence gathered by the State presented to the Courts in an open manner where the relevance and weight can be contested and assessed to determine if it proves his guilt - this isn't for him solely, but for everyone. It allows us to be confident that we are punishing the correct person, that he will not be subjected to an arbitrary punishment, and that LEOs are not fabricating evidence, and then beating people until they confess - because once you start down that path, its not so far to show trials for those who hold unpopular views.