On Monday, one of the top stories on Twitter (and nearly everywhere else) was about a doctor who was violently removed from an overbooked United Airlines flight to make room for a company staffer. Other passengers filmed the screaming man, who was bloodied and later removed from the plane on a stretcher, as he was dragged off the flight on Sunday evening. Before long, their videos racked up hundreds of thousands of views online.

According to another passenger, the doctor refused to give up his seat on the Chicago-to-Louisville flight because he needed to see patients the next morning.

In response, the Washington D.C. chapter of the American College of Emergency Physicians tweeted: "When you injure a doctor on a plane, @United, do you still ask 'Is there a doctor on the plane?' " The Twitter hashtag #NeverFlyUnited appeared thousands of times on Sunday and Monday, according to the social-media research firm Texifter. One typical post read: "You had a paying passenger beaten up on your plane. I hope he sues you for millions of dollars. #neverflyunited." Another: "Well, choosing an airline just got a hell of a lot easier. #neverflyunited."

Here's the statement United posted on Twitter on behalf of chief executive officer Oscar Munoz:

"This is an upsetting event to all of us here at United. I apologize for having to re-accommodate these customers. Our team is moving with a sense of urgency to work with the authorities and conduct our own detailed review of what happened. We are also reaching out to this passenger to talk directly to him and further address and resolve this situation."

Here's the statement the airline should have posted:

"All of us at United were horrified by what happened on Flight 3411 last night. We have reached out to the passenger to apologize, offer assistance and make amends. Nothing is more important to United than the safety of our passengers. This incident doesn't reflect our values and we're going to make sure it never happens again."

The company's actual response -- which doesn't include a direct apology to the injured passenger -- was probably influenced by lawyers worried about admitting liability. That's incredibly short-sighted. It's clear to any reasonable person watching the videos that what happened to this passenger was very, very wrong. By not fully apologizing, United suggests that it might believe otherwise. For anyone considering flying with the airline, that's a scary possibility.

United may think it doesn't need to worry about good consumer public relations because Americans tend to book flights on the basis of price. But plenty of travelers with expense accounts can choose to splurge on higher fares with airlines they prefer, and many more still try to pick a single airline to fly with to rack up their upgrades and miles in the same place.

So, what should a company do in a situation where it obviously has screwed up royally? The answer is simple. First, apologize immediately. And second, overreact to demonstrate that what happened doesn't reflect the company's values and how it conducts its business. In the case of this passenger, for example, United should offer full coverage of his medical expenses and free first-class flights for life for his entire family.

In my crisis communication courses, I teach my students that in such situations, they should think of an appropriate response and then "add a zero." It's a phrase I picked up from former Treasury Secretary Tim Geithner when I was a spokesperson for the department. Counseling his European counterparts on how to fix their sovereign debt crisis in 2010, he told them to add a zero to the 50 billion euro rescue fund they originally proposed. That's because the way to stem a financial crisis is by restoring confidence.

The same is true for companies. By immediately going overboard to make reparations to the passenger who was battered on their flight, United would have signaled to the people now using the #NeverFlyUnited hashtag that they know it's not OK to treat passengers this way.

Instead, United committed two cardinal sins of crisis management.

First, it chose not to take complete responsibility for the incident. True, it was a Chicago Department of Aviation police officer, not a United employee, who removed the passenger so forcefully. That officer has been placed on leave. But the passenger booked the flight with United, and instead of safely transporting him to his destination, the airline called police to remove him from its plane. Most ordinary people will think United was responsible for the incident and judge the airline accordingly.

Second, the company responded in doublespeak. The chief executive apologized for "re-accommodating" the man who was beaten up. What really happened is just the opposite: United was trying to re-book him on a different flight instead of accommodating his request to fly on the one he reserved. Munoz's statement reads as heartless legalese instead of a passionate denunciation of the incident and a promise to never let it happen again. That would help restore the confidence of United's customers.

Instead of adding a zero, United's team deserves one. This crisis response wouldn't pass muster in any of my classes.

* Alaimo is an assistant professor of public relations at Hofstra University and author of "Pitch, Tweet, or Engage on the Street: How to Practice Global Public Relations and Strategic Communication." She previously served in the Obama administration.