So the only thing stopping them from losing billions in a PR nightmare where they have extensive costs being racked up every day in two deepwater drilling rigs working around the clock, most of the deep sea submersibles in the world, plus a literal fleet of support vessels is a couple hundred grand for some magic plug, which they don't want to use, since they'll lose all that oil...
The conspiracy kinda falls apart really quickly, though. Have the oil spill out for a couple days, shut down the pipe with a 20 inch collet and a bolt, and then drill 'emergency relief wells' to suck up the oil. Seems a lot more cost effective and conspiracy friendly than letting the oil continue to spill out.
Odds are the reason why they haven't just 'cap and forget' the well is that it would be most likely that the pressures are so great that it would blow out the well pipe.
According to Michio Kaku, 22,000 lbs. psi.