Does Fram's ban on Wikipedia seem similar to recent events?
Only to an extent…
According to the BuzzFeed article referenced in the question, or the Slate article published a few days after, Fram was a highly controversial editor prior to his ban. To the point where one former member of the English Wikipedia's Arbitration Committee, a body of only 15 selected from over a thousand administrators ("moderators" in the Stack Exchange world), characterized Fram as an archetypal "toxic" user that the community's own laissez-faire attitude gave undue free rein.
Yes, banning Fram was clearly an overreach by the Wikimedia Foundation. They made an executive decision in a situation they had no business involving themselves in. In that sense the situation is similar. It was a decision they should have — very much so, and that's where the outrage stems from — entrusted to the community, i.e., that very same arbitration committee.
But the similarities end there: at the terrible decision made by the Foundation and its disregard of the community. The situation itself is very different: Monica was not, and is not, a "problem contributor". She's not a stand-in for "toxicity" on the site. She's an arbitrarily selected victim for a hypocritical "display of virtue" — by a person who, unfortunately, wields that kind of power. Monica is not, like Fram, a contributor whose behavior has long been heavily criticized by their peers.
What can Stack Exchange learn from it?
Stack Exchange, the company, can learn that it's possible to correct mistakes. It took the Wikimedia Foundation about three weeks to apologize and go back on its bad decision, then hand the matter over to the community — who, according to policy, should have handled it in the first place. This, after considerable pressure exerted on the Foundation's Board of Trustees by Wikipedia's founder, Jimmy Wales.
The Stack Exchange community can learn that non-profit foundations have different priorities than for-profit companies. Where Jimmy Wales acts as the gray eminence who regards Wikipedia as his legacy, Jeff Atwood and Joel Spolsky stay as far from controversy as they possibly can. It's been 6 to 8 weeks since the unceremonious and unjustified demodding, yet nobody at the company has taken responsibility and attempted to undo the damage. Even though it would cost them nothing. Other, hidden agendas are more important.