I have not participated in this thread as we just had our own "situation" in the North Sea.

Gullfaks C is the rig and one of her wells got unstable and spewed out Mud (well counterweight liquid). The BOPs (blow out preventers - yes we have several for each well) took care of the situation and temporarily "plugged" the well. It is now under control and has two cemented plugs, one deep in the well and one a bit higher. Last Sunday the string (pipe string) was cut and the second cement plug was installed Monday.
The cement will need harden sufficiently (full hardening process takes 28 days) before making a final analysis and declare the well safe.

I am involved with the maintenance of the equipment (owned by Statoil) used by drilling contractors on 6 oil platforms in the North Sea.

The big oil companies usually don't have their own drilling crews. They are contracted and the contractors have names like KCADeutag, SeaWell, Odfjell drilling etc... Most of them are local to the area we operate in.

The PTIL (governmental petroleum supervision agency) discovered discrepancies regarding maintenance routines on drilling equipment owned by Statoil but operated by drilling contractors and charged Statoil with the responsibility to fix it.
I am in the middle of a two year long project taking drilling into the Statoil system. I could tell a few horror stories but will refrain from doing so.

It is imperative that drilling equipment is sufficiently maintained. A BOP whether it is a 200 ton monster or smaller versions of it, needs a 5 year certification. It is dismantled from the rig and sent ashore every 5 years. It is probably the most expensive piece of equipment onboard an oilrig and the recertification cost a buck load.
It is very tempting to let the BOP run on overtime considering the expenses of stopping the drilling, get the thing off the rig, sent into shore and replaced with a spare BOP.
We have however in place a system where PTIL watchdogs can close the entire platform down if it operates with any equipment that has certification requirements and the recertification is overdue. But even so, I have discovered equipment that somehow has slipped through controls. Finding no previous recorded maintenance on critical equipment is rather disturbing.

I haven’t checked the APOS for our operations in the gulf, but I suspect there are governmental systems in place to oversee the oil operations in the US EEZ and make sure they operate according to procedures.