It has nothing to do with whether you know something is a crime or not. Many crimes require intention, such as murder and fraud, so you have to prove that to convict someone of that crime.

That doesn’t mean you can get away with anything as long as you don’t intend to commit a crime; there are many other crimes that don’t require intention at all, like involuntary manslaughter or gross negligence.

My point is that if you want to charge someone with a crime that requires intention, you have to prove that intention.

That's not what they are saying. They are trying to explain to you and others the concept of criminal negligence.