[RightWhale]

A "random" event in nature is like that. We don't know what the system "is." What we really mean is that part we are observing is "unpredictable."

In science, chemistry for example, a random sample would be exactly like the next random sample, all the same and predictable to any degree you care to measure.

[Alamo-Girl]

If the observation is qualified "as far as we are able to measure" - and if it is factually a "uniform distribution" - then there is no misleading.