I think anyone who watches network or cable news regularly realizes that the stations tend to get sloppy with reporting. An astute, informed interviewer would have corrected the First Lady’s misstatement; an informed reporter or anchor would have qualified the misinformation; erroneous facts, that are, in fact, not facts, get reported as facts anyway. Seems to be the norm of broadcast journalism anymore.
Editing a statement for the sake of time constraints sounds baffling. If the news medium doesn’t have time to quote what a speaker has to say, then why broadcast an incorrect, altered statement that changes the context of what was said?
I should get the same story if I’m watching Fox, MSNBC, PBS, or CNN; not a different version. I shouldn’t have to consult a fact-check site to find out what’s accurate.