Dao's attorney, Thomas Demetrio, said his client lost two front teeth and suffered both a broken nose and concussion after he was confronted by security personnel in an incident that sparked widespread outrage. Dao was not there.
Dao was one of four passengers randomly selected to be removed from the flight from Chicago, Illinois to Louisville, Kentucky on Sunday to accommodate the crew members.
Cellphone video of him being pulled down the aisle on his back and footage of his bloody face have created a public-relations nightmare for United.
"My dad is healing right now", said Crystal Dao Pepper, 33, one of Dao's five children.
"As a policy, WestJet does not deliberately overbook our flights", she said in an email.
The experience of being yanked off the Louisville-bound jet for Dao was more traumatic than when escaped Vietnam in 1975, the lawyer said.
The first-of-its-kind legislation from U.S. Representative Jan Schakowsky (D-IL) would abolish what has become deeply thorny territory for airlines.
United Vice President John Slater said he was not at liberty to say who called the aviation police, but ruled out the plane's captain. Sens. Tammy Duckworth and Dick Durbin were among 21 senators who wrote a letter to United and CEO Munoz demanding an explanation of United's operating procedure for deciding forcible removals, how often over the a year ago the airline has deplaned a passenger already onboard, and why a full $1,350 incentive wasn't offered to Dao, among numerous other questions.
Hacker unleashes late-night chaos throughout Dallas
The city has asked the Federal Communications Commission to help with the hard task of identifying a culprit. Officials hope to have the alert system back up and running by Sunday night or Monday afternoon.
She said what happened to her father "should have never happened to any human being, regardless of the circumstance". The airline also said all passengers on the flight would get a refund.
In a statement issued immediately after Thursday's news conference, United insisted that Munoz and the airline called Dao numerous times to apologize. He was discharged from the hospital late Wednesday, Demetrio said.
Thomas Demetrio, one of the lawyers, said Dao eventually would be planning a lawsuit and now was in a secure location healing from injuries he suffered while being drug off a Louisville-bound flight Sunday night.
"We'll file the suit when our investigative work is done", said Demetrio. But the attorney questioned its sincerity, suggesting United acted because it was taking a PR "beating". After what happened, Dao "has no interest in ever seeing an airplane" and will probably be driven to Kentucky, Demetrio said.
Three Chicago Department of Aviation officers are on leave following the incident, and the airline's stock plummeted amid boycott threats.
Chicago aldermen on Thursday grilled United Airlines city aviation officials about the now-infamous incident at O'Hare Airport when a paying customer was dragged off a full flight.