The lowest known point in the Challenger Deep is 10,911m below sea level.
Unless they started 1350m or so above sea level, he's gonna hafta do some serious digging down there to make up the difference.
The Kola Superdeep Borehole set two records: deepest point reached, and longest borehole. The latter record was, as you say, surpassed twice by oil operations. But if you look at the context of the comment I was replying to, it's clear that Dr Stalker was talking about deepest point reached (surely no one thinks Cameron could dig a multiple-kilometer hole from his submarine). And so it is the deepest-point-reached record that is relevant, which was not surpassed by oil operations. This is because those oil boreholes are diagonal, with a large horizontal component.
Also, based on the information I could find, I don't actually know how deep the KSB is, relative to sea level, because I don't know what altitude its "ground level" is, and all the depth measurements I could find are relative to ground level.
The deepest oil well that I know of is BP's Tiber well: http://www.bp.com/genericarticle.do?categoryId=2012968&c..., 10685 m but probably measured from the rig floor, so about 9400 m actual drilled depth, starting 1259 m subsea.
By the way, the extra amazing thing about the Kola well is that core was collected over the entire well depth. This means that the drill string had to be pulled out hundreds of times during drilling to recover the core, and explains why the project took 20-odd years to complete.