They are comparing it to using mines which would obviously be cheaper.Is it possible that similar thing could happen with uranium mining as Aberfan (You seem to have confused coal mining with the use of coal which although related are not the same) - why not? It's a mined product, so there's of course a possibility it could.
We don't actually have any uranium in this country that is actively mined so it's unlikely to happen in this country though.
As for burying it in boreholes then it's been looked at and it was deemed to be too expensive and no one could give any guarantees that it wouldn't cause problems (Presumably people who know more about it than you or I) - so again, to say that there is simply no problem as "It's totally sealed" is just not right.
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Nuclear waste disposal: Why the case for deep boreholes is ... full of holes
A start-up in California wants to use directional drilling technology to put America’s spent nuclear fuel into deep boreholes. But such a solution won’t be cheaper, safer, or any less politically toxic than a mined storage facility.thebulletin.org
As I have mentioned before the Boulby mine mine would be perfect and would take all of Britain's current and future waste
Some of the tunnels are more than 4,000 feet deep under the North Sea.
When the halite is removed the tunnels close back up due to the immense pressure sealing things permanently in solid rock.
How could that be a problem?
The mine is well up for it but nobody will give it considering due to prejudice and nothing more.