When I see the word "random" I parse it as "unpredictable", since this is usually what people mean (even if they don't realise it) and can clear up many arguments. The concept of 'random' is interesting in some cases, but the vast majority of the time it's far stronger than what is required.

In this case, the question is:

> If a number generator is uniformly distributed, why might that not be 'random enough'?

If we rephrase this as:

> If a number generator is uniformly distributed, why might that be 'too predictable'?

This makes the flaw obvious: there are many ways to choose numbers uniformly which are completely predictable. For example, choose the smallest value first, then choose a value which is furthest from any previously-chosen value (in, say, lexicographic gray-code order).

The point here is that 'uniformity' is not the property we care about; it is a consequence of the property we care about (unpredictability). If a distribution were non-uniform, we would be better able to predict it (by biasing out predictions to match the distribution), hence the least-predictable distribution is necessarily a uniform one.

Other times this comes up:

> Are quantum measurements 'truly random'?

That's untestable, but we can test whether they're predictable or not.

> This encryption algorithm requires a source of random bits.

It would work just as well with a source of bits that are merely unpredictable.

> This strategy can only be defeated by a random opponent.

It can also be defeated by an opponent which you can't predict.

And so on.