Perhaps the difference is that UBI doesn't pay you for working. In your counter-example, for the UBI to result in the same thing requires that the worker work exactly the same number of hours. UBI is usually per-person, not per hour worked.

If you tie UBI to per-person, for better or for worse, you distort the market to increase the price of labor. Each person has to work fewer hours to have the same income as before, thus you'd likely see less labor supply and thus higher price.

By tying UBI partly to labor, for better or for worse, you distort the market to decrease the price of labor at least in comparison to per-person UBI. I'd imagine vs. the status quo it's an price increase, but stacked against per-person UBI it should generate more labor supply and thus a price decrease.

If made independent from livable wages, it isn't clear that increasing the price of labor is optimal at the moment. It would seem to accelerate the pace of automation which would increase the pace of inequality. It would also slow overall economic output - the $11/hour generating job may cease to exist.