I delayed responding to this, as requested by @swamidass
It is unclear what you are expecting when you ask for “rigorous support”. I am just using “random” in the ordinary way.
Think of a Las Vegas casino. They have roulette wheels that they spin for a random outcome. If they were to spin those roulette wheels twice as often, they would still produce random outcomes. What you quoted from Shapiro was about the rate of mutation. Changing the rate of mutation is like spinning the roulette wheel twice as often. The rate of producing random outcomes will increase, but they are still random outcomes.
I did not question any of his empirical assertions. I only questioned his characterization of them.
I have read Shapiro’s book, though it was a while ago. My main disagreement was that he tended to overstate his conclusions. I agree with Shapiro view, that there is intelligence in the cell.