I think you're missing the point that you can just put uranium into a lead box and give it to someone else. You don't have to own a uranium mine to possess uranium.

You also have to realise that there are places in this world which are impossible to track and enforce nuclear non-proliferation. The UN recognizes they can't do anything about this (and it's laughable to think the UN would do anything, anyway).

The idea of nuclear non-proliferation is bunk. It's bunk because (aside from just propagating the founding countries' nuclear hegemony) it's completely unenforcable. There's also, within the NPT, the gigantic loophole which promotes the inalienable right of all countries to pursue nuclear energy. There's very little to stop anyone from using fissile materials from nuclear reactors in creating weapons.