Really it boils down to the fact that (to quote a very insightful comment I can no longer recall the author of) “if I flip a coin and look at it whilst hiding it from your sight, the outcome is perfectly deterministic for me but it is still perfectly random for you” (and, I'll add, the maximum speed at which I can “de-randomise” the outcome for you is by telling you what I measured (at the speed of light)).
No, there really is a difference between a flipped coin and an unobserved particle: the latter can interfere with itself. A coin will not interfere with itself after you flip it even if you don't look at the outcome.
Fair enough: single-particle-at-the-time double-slit-experiment is relevant here, but I didn't have it in mind when I was thinking of remote entangled particles being measured. My bad.
This is just getting at the basic insight that probabilities are most usefully thought of as being subjective. The coin will land on either side depending on the torque applied and air resistance and whatnot. 50% is only a measure of our subjective uncertainty. This isn't about quantum mechanics.
