I admit my mental model could be totally wrong, but I assumed that nuking the spill at the leak site would in essence "cauterize" the leak as there'd briefly be a layer of molten rock covering the entire leak area that would then solidify.

It doesn't intuitively seem like the well for the nuke would have to be as deep as the relief well, but I have no experience in deep-sea drilling, so this could be a total misconception.

Also, I'd image the Russians' claims of having stopped the leaks with nukes would have been verifiable.