> [that clarification] was given in the context of a modified problem
I don’t understand what do you mean by that. The clarification was part of the original answer in the context of the original question. The clarification was stated again and again and again. If that’s a “modified problem” so be it but that was the problem being discussed with her readers.
Ok, so the modification was the "Here’s a good way to visualize what happened." explanation.
I would say that the whole (short) paragraph is intended to clarify why the answer to the question is "Yes; you should switch."
Maybe it was not a good way to visualize what happened after all. Experience shows that some readers were unable to understand the argument.
However, none of them complained about the explanation being wrong because those were two completely different problems (only in the second one the host will always avoid the door with the prize, apparently).
I don’t understand what do you mean by that. The clarification was part of the original answer in the context of the original question. The clarification was stated again and again and again. If that’s a “modified problem” so be it but that was the problem being discussed with her readers.