However, many other countries do not have presumption of innocence in their constitution or charter of fundamental rights. The US has a very different approach, as suspect are told the Miranda Rights ("You have the right to remain silent. Anything you say can be used against you in a court of law, etc.") which somewhat presumes the suspect NOT to be innocent.
Actually, the presumption of innocence is a very important part of the American legal system. Mirandizing suspects when they are arrested is so they are aware of their rights, and that they are not required to say anything at all to the police. Suspects who are not mirandized and confess without knowing their rights could later claim that their rights were violated, making their confession inadmissable in court. It is for this reason that it's very important to follow this procedure, it's not an implication of guilt, it's standard protocol.

In fact, the suspect does not have to say anything at all in his defence at the trial; all of the burden is placed on the prosecutor to prove beyond a reasonable doubt that the accused is actually guilty of the crime. If they cannot do that the defence can rest without uttering a word.