Hetherington insisted that the board are backing their management, despite the fact that they have nine defeats from nine to show from a very difficult season.
He said: "You can do without that type of reporting. It was claimed to come from 'a source close to the club', but there are no sources close to the club.
"There's just the club and we are all in this together.
"There will be no knee-jerk reactions from us. We are committed to doing what we did last season, which was a tremendous fightback in the second half of the season to achieve safety.
"We are seven points adrift, but there is a lot of rugby to be played yet. I'm the chief executive and I am saying that we are working together to improve and turn this situation around."
Leeds rugby director Andy Key said: "It's great to hear Gary say what he said, because when you read stuff like that about 'Backy' it just does not help anyone.
"We have always felt that the board are behind us, which is a great help when you are struggling. There have been some positives from every game. It is just a case of us getting that breakthrough win and the confidence levels rocket upwards."
The home side earned a bonus point by scoring four tries long before the end, a haul that moves them up the table and a step closer to the pre-season ambition of rugby director Conor O'Shea, who insisted they were potentially a title-chasing team. For Leeds, though, the winter will be long and hard as they battle for survival.
Harlequins began the day ninth in the table having managed only a draw from their three previous Aviva Premiership games.
But it was the visitors who reacted the sharper in freezing weather, punishing a sloppy start by their hosts who presented Leeds possession from the kick-off. Under pressure, Quins went offside and Leeds fly-half Ceiron Thomas scored the penalty.
It took only four more minutes to see why Leeds are struggling, however. Having turned over Quins ball, it came to Rhys Oakley whose attempted pass to his left was intercepted by Chris Robshaw, afforded a free run-in for a try which was converted by Nick Evans.
Mike Brown broke out from the back and managed to off-load for Robshaw to find loosehead Joe Marler. The prop attacked the Leeds defence, drew two men and flipped a fine ball inside for scrum-half Karl Dickson, who scored at full pelt. Evans again converted and added a penalty on 21 minutes as Leeds grew visibly more fragile under pressure.
The sole consolation for under-pressure head coach Back was that his players were up for the battle, if lacking the necessary quality to actually win it.
That determination paid off when Thomas added his second penalty of the game but Evans replied in kind four minutes from half-time, and his next score was extra-special. Quins retained possession for phase after phase until Brown collected a ball thrown over his head by Dickson from the Leeds line which changed the point of attack, and Evans took Brown's inside pass to dart over by the post before converting his own try.
The problem facing the Leeds management remains their need for someone or something to lift them, to give the players real belief in themselves.
After a decent start, it took only one intercepted pass to leave collective chins on the floor and by the break, the game was over as a contest.
All the more so when Tom Guest stormed forward six minutes after the break and simply shrugged off two weak tackles to score. Evans added the conversion as the crowd celebrated the bonus-point fourth try.
Credit Leeds, therefore, for battling back to score a try on 50 minutes when Lee Blackett finished off a strong move involving lock Tom Denton, whose drive set up the opportunity as Harlequins backed off. Thomas missed the conversion.
Dickson set Brown up to finish in style before a break out saw Blackett score his second try of the game, Thomas converting, a score that showed the team's character at a time when it would have been easier to try to wind down the clock.
Ross Chisholm and Dave Moore completed the rout.
Key added: "We are massively disappointed because we have come here, scored two tries yet left empty-handed.
"Why? Because of our own basic errors. The history of this season is littered with our basic errors proving so costly. It just means our efforts have to be stepped up even further."
Harlequins: Brown, Lowe, O. Smith (Chisholm 46), Turner-Hall, Williams, Evans (Cleg 65), Dickson (Moore 70); Marler (Jones 55), Gray (Brooker 52), Johnston (Lambert 55), Vallejos Cinalli (Kohn 52), Robson, Robshaw, Skinner, Guest (Browne 68).
Leeds Carnegie: Stephenson, Blackett, Fa'afili, S. Barrow (MacKay 57), Wackett (Hinton 68), Thomas, Mathie, Hardy (Alonso 40), Nilsen, Gomez (Swainston 52), T. Denton (Paul 65), Wentzel (Black 74), Myall, Oakley (To'oala 65), Browne. Unused replacement: Denman.
Referee: Martin Fox (RFU).