What people are ignoring, is that with a mud weight of between 14.1 and 16.8, depending on sources, the well was under control, even though the plug was compromised.
Put that same hydrostatic pressure on the formation, and it will be shut in again. then the new plug can cure. The rest, once you can put the fluid in the wellbore, is just a math problem.
The same fluid column (drilling mud) will be exerting hydrostatic pressure in the relief well, holding the formation fluid back.
The problem on the Deepwater Horizon came about when the riser pipe was displaced with seawater (despite apparent indications that cutting the hydrostatic pressure on the formation was letting the well flow, indicating a bad plug), flow indicators were ignored, and the well blew out. The displacement with the lighter seawater reduced the hydrostatic pressure on the formation downhole by some 2200 psi, letting the well blow out.
See my post 19 about GE’s technology - interesting stuff.
Your talk of mud reminds me of a funny story. Some salesman/technician from the company that sold our oil well the bentonite “mud” gave a “lesson” to all of us on how to measure it, calculate how much weight you need, remeasure, etc. (It was a slow day!). After about a half-hour of our “lesson”, our experienced mud man, who had been holding his tongue the entire time, said “So, if I don’t add water, it’s just dirt - right?”