However, the term "random" is rooted in mathematics. The issue is not a "quibble" of philosophy, it is a matter of "proof" and accuracy in speaking.
If one pointed to a rectangle with four right angels and parallel, equal sides and declared it a "trapezoid" we'd say "Not so fast, it is a square, a trapezoid has only two sides parallel and it does not have four right angles."
Likewise, if one points to a thing and says to me it is "random" I'll reply "If you have established a uniform distribution, then perhaps so, but only to the extent of your measurement - because you cannot say something is random in the system unless you know what the system 'is.'"
a propos "accuracy in speaking": We were talking (at least, I was) about the physical world, not the mathematical. And there we're talking about experiments - not proofs. And until now, no experiment has falsified the hypothesis that the quantum world acts randomly...