I don't think the story disproves or is inconsistent with Boehner's version.
The plan may well have originated with the Republicans, but this story is not definitive proof that it did.
Maybe's Maddow's film clips are. I don't know. I did not see those.
ETA: After I posted, I saw this, FWIW:
The bill was the final chance in a series of proposals to resolve the 2011 United States debt-ceiling crisis, which featured bitter divisions between the parties and also pronounced splits within them. Earlier ideas included the Obama-Boehner $4 trillion "Grand Bargain",[13] the House Republican Cut, Cap and Balance Act, and the McConnell-Reid "Plan B" fallback. All eventually failed to gain enough general political or specific Congressional support to move into law, as the midnight August 2, 2011, deadline for an unprecedented U.S. sovereign default drew nearer and nearer.[14]
Ultimately, the solution came from White House National Economic Council Director Gene Sperling, who, on July 12, 2011, proposed a compulsory trigger that would go into effect if another agreement was not made on tax increases and/or budget cuts equal to or greater than the the debt ceiling increase by a future date. The intent was to secure the commitment of both sides to future negotiation by means of an enforcement mechanism that would be unpalatable to Republicans and Democrats alike. President Obama agreed to the plan. House Speaker John Boehner expressed reservations, but also agreed.[15]
On July 26, 2011, White House Budget Director Jack Lew and White House Legislative Affairs Director Rob Nabors met with Senate Majority Leader Harry Reid to discuss the plan. Reid, like Boehner several days before, was initially opposed to the idea, but was eventually convinced to go along with it, with the understanding that the sequester was intended as an enforcement tool rather than a true budget proposal. [16]
http://en.wikipedia.org/wiki/Budget_Control_Act_of_2011
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