Speaking on Facebook, Naughton's friends claimed he was removed and later banned from 'all English cricket' after Broad told a steward about the incident.
However, Naughton has denied this - saying the matter was dealt with 'civilly'.
He gained entry into the Long Room because his home club in Australia has reciprocal status with the MCC.
Naughton's friends on Facebook have claimed he was banned from Lords following the incident and stripped of his MCC reciprocal entitlement.
But speaking on Tuesday, Naughton said: 'With Facebook many stories are over-exaggerated and this is another of those.
"Unfortunately it seems many Australians still have hard feelings over the Stuart Broad incident from many years ago as you can see from the posts.
"I will however tell you there was a very small incident, none of which resulted in me being ejected from the MCC members nor getting my membership revoked and was resolved very civilly.
"After which my girlfriend and I stayed until hours after the close of play and mingled with players from both sides afterwards. It was a very enjoyable day for both of us."
Naughton made his remark during the recent Ashes clash between England and Australia, which the hosts lost by 405 runs.
The England Cricket Board refused to comment on the matter, and said: 'This is a matter for the MCC.'
A spokesman for the MCC confirmed the incident took place, but refused to elaborate on the matter.
They said: "We would never comment on specific disciplinary proceedings, but I can confirm the gentleman concerned is not a member of the MCC and we believe the matter is closed."
Broad has become something of a pantomime villain among Australia's supporters after an incident during England's Ashes series victory in 2013.
During England's tense victory in the first Test at Trent Bridge, the Nottinghamshire star refused to walk off when given not out by the umpire despite clearly hitting the ball with the edge of his bat.
Australia fans took this so badly that Broad was targeted with accusations of cheating and at times foul insults during the following series Down Under, which Australia won 5-0.
One local newspaper even refused to publish his name ahead of and during the first Test in Brisbane.
-DAILY MAIL