For one thing, when a defendant pleads guilty, guilt is *never proven*.
For another, there are a large number of guilty pleas by innocent people.
And for yet another thing, many criminal convictions rest on no evidence except for police eyewitness testimony, which does not constitute proof.
And for yet one more thing, police testimony has been shown to be likely false in at least hundreds of thousands of cases.
What's most interesting to me is that the assumption that our justice system presumes innocence is taken as an article of faith, quite unlike the assumption, say, that politicians represent their constituents. That is taken to be an ideal principle, sometimes met, but it's not presumed to be met, by and large; even in polite society, everybody knows that politicians frequently represent their donors, entrenched wealthy interests, organizations that get out the vote (like unions), and themselves.
I consider this sort of misleading assumption a "Brinkleyism", after centrist Columbia history professor Alan Brinkley, who muddles all sorts of forgiving assumptions about the workings of power in the United States with the official story that the U.S. power structure has constructed to guide thinking away from understanding its workings. Although you could also call them "The Economist-isms" after the venerable, self-congratulatory, and frequently obfuscating London publication.
For instance, the assumption that police must get a search warrant to force entry to a property, or the notion that Americans didn't like being ruled without representation by King George, or the idea that the U.S. government has long fought against terrorism, or the story that the U.S. government opposed socialist governments taking power for humanitarian and democratic reasons. The more you learn about how politics and justice play out in real life, the more you realize how misleading, inadequate or flat-out wrong these centrist presumptions are.