I agree with you 100% that they're not independent, but I don't know enough about the data to model the probabilities of failure and availability in a HN comment :-)
After today's event, it would certainly be interesting to see how resource consumption changed in other availability zones and at other providers during this outage.
I wonder if that could be measured passively? What I mean is, by monitoring response times of various services that are known to be in specific regions and seeing how that metric changes (as opposed to waiting on a party that has little-to-no economic benefit to release that information.)
In practice, that's not true, and it's not true enough to ruin the entire rest of your calculations. For Amazon regions to function independently, they'd have to be actually, factually independent; there is no interaction between them. The reaction to one node going down is never to increase the load on other nodes as people migrate services, etc. There's fundamentally nothing you can do about the fact that if enough of your capacity goes out then you will experience demand in excess of supply.
If you want true redundancy you will at the very least need to go to another entirely separate service that is not Amazon... and if enough people do that, they'll break the effective independence of that arrangement, too.
(This is a special case of a more general rule, which is that computers are generally so reliable that the ways in which their probabilities deviate from Gaussian or independence tends to dominate your worst-case calculations.)