A Squared:
I never claimed it was legal to descend to MSA in the US. As others have pointed out it's not a procedural altitude in the US I'm only saying that if they had descended to the relevant MSA and maintained that altitude until established on the approach, (which is what is being proposed by the OP) they would not have crashed. That's not a trivial distinction.
Having been trained many times by the same training department that trained the TWA 514 crew, I doubt they had any training on MSAs, or even how to pick them off the Jepp chart (which portrayal of MSAs was quite bad in those days.) They focused on three critical altitudes in the plan view leading to ROUND HILL. Had they selected any one of those three altitudes as their minimum altitude until ROUND HILL, they would have been home free. Some on the accident investigation team speculated that the ride was so bad they wanted to get down. No one will ever know if that was in the captain's mind.