The corpus delicti rule states, if I understand it correctly, that there must be evidence that a crime occured (other than a confession) before anyone can be convicted of that crime. I have found claims online that the corpus delicti rule is applied at least in parts of the United States. (1, 2)
However, the United States has a plea system that allows for a person to be convicted without a trial ever starting if the defendant pleads guilty (At least, that's how I understand it, I'm not from a common law country). This seems to be a contradiction to the corpus delicti rule because no evidence of the crime was presented to the court before the conviction.
So my question is: Does corpus delicti really apply in the U.S. or is it possible to circumvent this test completely by means of a guilty plea?