> It skews the distribution a tiny little bit, ...

But it doesn't - that's the point ;-)

If double-rounding doesn't occur at all (which appears to be the case on most platforms), absolutely nothing changes (because min(int(random() * N), N-1) == int(random() * N) on such boxes).

If double-rounding does occur, double-rounding itself may change results "all over the place", and I haven't tried to analyze what effects that has on the distribution.  In the comparative handful of cases where int(random() * N) == N on such boxes, clamping that back to N-1 just yields the same result we would have gotten on a box that didn't do double-rounding.