"Nuking does not clear a level" - this is the description in bagdes guide (which you can find HERE) about Lava Pits. And any special level, btw.
If special levels should not be considered “cleared” when using a nuke, then there's another bug: In the same game I nuked the Spiders' Lair and it worked.
In many cases and, in particular, levels that are quite difficult to finish without nukes, it has been shown through mortems that using a nuke to destroy everything in the level doesn't give you the "Complete [level]" badge. This may not be the case for ALL of them, however. I know that it's proven for Mortuary, UC, and Vaults, which also happen to yield the most difficult badges. (Arena doesn't but, as you may notice from the guide, I don't consider it much of an issue.)
If you have a mortem showing that you nuked Spider's Lair and still got the badge for it (Bronze or Silver, probably doesn't matter) then I have something to go off of. The same would be true of Lava Pits, The Wall, and City of Skulls, so anything relating to them would be helpful, both for my guide and any possible bugs.
If the game isn't coded such that nuking invalidates the badge of completion, I would prefer that the aforementioned be added. Otherwise, a reply in the Badges Guide thread would be appreciative.
EDIT: I should also mention that my guide is still a work-in-progress, and should not necessarily be used to confirm problems with the game itself. A few versions back I had to correct a mistake that stated any badges with the words "standard game" could not be gained through partial victory, even though they can (half the people who have done Strongman Silver would know). If Kornel ever feels like correcting something in the guide when I have it wrong, that'd be awesome, but until then, most of it is only in the "likely correct" category.