"Their point is that no non-violent movement has ever succeeded in a vacuum. There have always been parallel violent movements that essentially scared the powers that be into negotiating with the more moderate non-violent movement."
I think that's pretty clearly nonsense. What were the "parallel violent movements" in the People Power Revolution (1986, Philippines), or most of the Eastern European revolutions of 1989 (such as rather aptly named "Peaceful Revolution" in East Germany and the "Velvet Revolution" in Czechoslovakia), or the overthrow of Slobodan Milosevic in 2000, or the 2003 Rose Revolution in Georgia, or the Arab Spring in Tunisia? (For that matter, how was Malcolm X actually "violent"?)
On the general question of whether violent resistance is effective, you might want to take a look at the well-regarded study by Maria Stephan and Erica Chenowith on the relative success rates of nonviolent and violent resistance campaigns. You can find the original 2008 study here; it was later expanded into a book in 2011 called Why Civil Resistance Works: The Strategic Logic of Nonviolent Conflict.
They looked at a total of "323 nonviolent and violent resistance campaigns from 1900 to 2006". (These were generally independence movements or movements aimed at overthrowing a repressive regime.) Nonviolent movements were twice as likely to succeed as were violent movements. In addition, nonviolent movements were significantly more likely to result in democratic successor states; successful violent movements were more likely to result in oppressive regimes, presumably because groups that rely on violence to succeed tend to continue using the same tactics and mindset after they win.
One of their main arguments is that violent campaigns are less likely to get popular support (or international support) and are easier for regimes to suppress without much protest. Put more simply: if your movement is violent, you're less likely to get the general public or international groups to support you, and it's easier for the regime to portray you as illegitimate and too dangerous to talk to, and easier for them to justify and get away with suppressing you. One implication of this is that if the regime can link (legitimately or just via propaganda) a nonviolent movement to a violent group, it can poison the nonviolent movement in the eyes of the general public, making it less likely for them to succeed. (This is in part echoing Opt's answer.)