Julian Cole, who was 19 at the time, got into a confrontation with a bouncer and the officers after being ejected from Elements in Bedford in May 2013.
After trying to get a refund, he was brought to the ground twice – once by the bouncer and once by the officers.
His broken neck was only discovered after he had been carried to a police van and driven one mile to Greyfriars police station.
He subsequently went into cardiac arrest and suffered brain damage. He is now in a vegetative state and needs 24-hour care.
PCs Hannah Ross, Sanjeev Kalyan and Nicholas Oates falsely claimed he had been able to walk to the police van.
But CCTV showed he had to be carried, with his legs dragging on the ground and his head hanging down. Witnesses told the same story.
The officers also claimed Mr Cole could move his legs and put a trainer back on while in the van.
He was unable to stand after arriving at the police station, and PC Ross called an ambulance a few minutes later.
At a misconduct hearing, the PCs were found guilty of gross misconduct for lying about the teenager’s condition.
Another officer, Sergeant Andrew Withey, was found guilty of misconduct for failing to carry out proper welfare checks, and given a final written warning.
Mr Cole’s mother Claudia said the family “suspected a cover-up” when a police officer said her son had been “chatty” in the police van.
She added: “This tribunal’s decision makes it clear that not only did the officers lie about events involving Julian, but they showed an inhumane indifference to his welfare.
“We won’t stop until we know who put Julian into a vegetative state, and until they have had to answer for what they did in a criminal court.”
The Crown Prosecution Service has already said that no criminal charges will be brought forward.
But the family’s solicitor, Rachel Harger, said “fresh evidence has come out during the course of the hearing which will assist the family as they seek answers as to who caused the injuries Julian suffered”.
Mr Cole’s relatives are expected to ask the Independent Office for Police Conduct (IOPC) to reopen its investigation into what happened.
IOPC regional director, Sarah Green, said: “It will never be known exactly how (Mr Cole’s) neck was broken, or if swifter care could have prevented the awful consequences of the break.
“The panel today have concluded however that the officers failed in their duty to provide adequate welfare checks, and worse, that three of them were dishonest in how they presented their version of events.
“This dishonesty has only added to the anguish of Mr Cole’s family.”
Bedfordshire Police Assistant Chief Constable Jackie Sebire said: “It is clear that no evidence was found that any of the officers involved were in any way to blame for the catastrophic injuries suffered by Mr Cole.
“This misconduct hearing focused on the actions of our officers in the care given to Mr Cole and their honesty and integrity in the events following his injury.
“I apologise that their conduct following the incident fell well short of what we expect at Bedfordshire Police.”