Earlier quoted context omitted.
https://en.wikipedia.org/wiki/Randomized_controlled_trial The same thing it means in every context: that (with enough samples) you can control for confounders.
Supposing that patients did better in the morning because, say, the nurses were more alert, no matter how many samples you take you'll find the patients do better in the morning. How does "more samples" help control for confounders rather than just confirm a bias?
I think you're correct that randomising patient assignments doesn't control for provider-side confounders. Curious if the study also randomised nursing assignments.