We don't have reason to believe that. Even Uber now agrees that more simulation should have been done, and they're trying to catch up. All the necessary data for this could have been gleaned from instrumenting human-driven cars, and then testing the object recognition, object avoidance, and other driving algorithms against the resulting data.
Uber's Arizona death wasn't "human error". It was negligence. They also weren't "behind schedule" in any meaningful sense; some exec picked a too-aggressive goal, and people cut corners in a vain attempt to meet it. They shouldn't just be paying a "market price". They should be facing charges for criminal negligence leading to involuntary manslaughter.
If Uber was more focused on doing things the right way their program would be much further ahead.
The data and experience gathered from real-world testing should (I'm not saying "will") accelerate the progress to the point you mention - "once their error rate drops below that of a human driver".
Let's look at the Uber case, since everyone infers so much from it. One fatality. One. And the program was immediately shut down. And how did it happen? Engineers had deliberately disabled the automated emergency braking system to reduce "erratic behavior", but had no automated notification to the driver. And the driver was distracted, doing data entry for the test as he was instructed to do. If the emergency braking system had been on, it would have stopped the car on time - they have the data for this.
This sure looks like human error to me.
And that single accident put Uber's program drastically behind schedule, relative to more cautious/thorough competitors. Uber paid a market price for its eager carelessness.