I'm in no way an expert on oil well drilling, but I did do a little Internet research on the methods of installing "balanced plugs" in oil wells. It looked to me like it is often standard procedure to install a plug with the mud still in place.
For instance, if the mud is being circulated down through a central pipe and out through the "annulus", they only have to insert a measured slug of cement in the mud stream, and knowing all the volumes, stop the stream when the cement is just at the bottom and is balanced in the central pipe and annulus. Then they withdraw the central pipe and let the cement cure.
I think what happened was that a previously undetected reservoir of nat gas found it's way to the well and began expanding, pushing the oil and anything else in it's way out to the surface. The well went out of spec. They did not catch it in time and likely could not have stopped it anyway. Then the BOP failed and that was that.