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I've read all over the place that two people receiving the same address is so astronomically high as to be almost impossible. But reading this question it seems that it's actually very possible that two people share the same address. Even if everyone has a different private key it will necessarily happen that two people will share the same address. Am I missing something?

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It is indeed 'very possible' that two people share the same address. It is also extremely unlikely to happen with an astronomically small chance.

Yes, the chance may be much larger than two people sharing the same private key, but that does not mean it is large.

Ethereum addresses have 40 hexadecimal digits. Each digit can have 16 possible values. This means that the amount of possible addresses can be calculated like this:

16 ^ 40 = 1461501637330902918203684832716283019655932542976

Let's assume that all 6 000 000 000 humans each have 10 addresses.

The chance of you generating one that someone else already had is:

(10 * 6000000000) / (16 ^ 40) * 100%
=
0.0000000000000000000000000000000000041053665947 %

As you can see it's slightly misleading to describe it as very possible, and it will certainly not necessarily happen.

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