Thats not how law works.
Unfortunately it's exactly how the law works in the United Kingdom, and it's working towards being like that in the United States with changes in a number of states (including NY and CA).
The key change is that the onus is put on the accused to prove consent (which can almost never be done) instead of the standard innocent before proven guilty approach where the lack of consent has to be proven. This is being called "affirmative consent" and "yes means yes" in a typical PR/propaganda play.
The incentive structure that this sets up is pretty interesting. For one, it provides men with incentives to record every single sexual encounter they ever have.