Not all randomness is quantum randomness, even if everything includes a -component- of quantum randomness.

The issue is that "randomness" is a poorly-defined word. You're letting different, and opposing, definitions of randomness bleed together here (and probably in your thought processes as well). Taboo "random"; you'll rapidly see the issue. You're including chaos - that is, an essentially deterministic outcome that is impossible to predict due to the number of variables - randomness in with your quantum randomness.

ETA: You -can- define a problem such that quantum randomness applies instead of chaos randomness; simply state that the outcome of the coin flip is dependent upon an unobserved quantum event, that, say, may interrupt a single nervous signal which determines whether the coin comes up heads or tails. However, this problem is pretty far removed from the problem of coin flips in general; the coin becomes wholly unnecessary.