That's separate and has no bearing on the burden of proof, which is ALWAYS on the prosecution. It is legitimately shocking that educated Americans can be ignorant of the most basic tenet of our justice system, the presumption of innocence.
The prosecution has the burden of proof to establish the basic accusation, and the defendant is always entitled to offer the negative defense of "I didn't do it". For instance, if I'm accused of killing Paul, I can always say "I didn't kill Paul" and the prosecution has the burden of proof to say that I did. On the other hand, if my defense is that I killed Paul in self defense, the burden of proof is on me to show that my actions satisfied the legal definition of self defense in my state.
I guess no crime can ever occur then, since you can never prove it wasn't consensual?
Oh you were caught in 4k walking down the street smashing every windshield with a crowbar. But how can they prove all the car owners didn't pay you to do that for a film project?
I have no idea what you want me to say. The presumption of innocence is the most basic, fundamental, indisputable element of the US justice system, it dates to the Anglo-Saxons, and it's part of the Universal Declaration of Human Rights: https://www.prosecutorintegrity.org/innocence/cornerstone/