That article makes the same unstated assumption, attempting to treat `random()`'s output (and transformations thereof) as true random variables. But it just changes the rounding mode and bin size in a manner that _happens_ to work better for some transforms like log.

It changes the fundamental property of the distribution — the cdf — without stating it.

With floating point realizations of [0, 1) intervals:

   cdf(p) = P(random() < p) := p

With (0, 1] intervals:

   cdf(p) = P(random() <= p) := p