Director-General of the GAA, Páraic Duffy, has claimed that fans entering the pitch after the game is a "bigger problem" in Croke Park, but there will be no change in the association's official position on forbidding access to the pitch after games.
Referring to last Sunday where he had the best seat in Clones to watch his native Monaghan end a 25-year Anglo-Celt Cup drought with victory over Donegal, Duffy said: "Look, I enjoyed the experience last Sunday, it was fantastic to see Monaghan supporters on the pitch, but it is dangerous.
"It's great when it goes off well, but there will be no change in our position in that."
Duffy was speaking at the launch of the All-Ireland quarter-finals at Glenswilly, the home club of Donegal captain Michael Murphy.
Last Sunday brought emotional scenes as Monaghan fans flooded the field afterwards in jubilant celebration.
A week before, Limerick hurling supporters did the exact same following their win over Cork in the Munster hurling final.
Asked his views, Duffy commented: "The reason for us saying no to pitch invasions is that it's a health and safety issue.
"It wasn't a particular issue last Sunday because in Clones you'd 30,000 people and the week before in Limerick you'd 40,000 people.
"But in Croke Park you potentially have 80,000 people coming on to the pitch," he explained.
"So it does create huge problems in Croke Park," he added.
The notion of fans coming on to the pitch to celebrate victory in Croke Park was ended in 2010 when fences were erected at the bottom of Hill 16 and a heavy stewarding presence encircled the field, while the first few rows of seats were also covered in mesh.
"It's a bigger issue in Croke Park than anywhere else because you have a huge number of people going on to the pitch.
"This is not a GAA crusade and it was a case of us acting on Garda advice," acknowledged Duffy (right).
"The problem is in Croke Park when you have huge numbers of people there.
"You have potentially 80,000 people there.
"In Clones you have potentially 32,000 people there. Pitches are broadly the same size," he said.
"The other huge problem with Croke Park is when people come on to the pitch, they all go out on to Jones' Road and that's what brought this to a head – when crowds are facing in different directions, there is a problem outside of the stadium as well as inside," he added.
While last Sunday may have been pleasant viewing for Duffy, the night before he was in Newbridge for the qualifier tie between Tyrone and Kildare and was upset with how referee Joe McQuillan was treated as he made his way through the crowd to the referee's changing rooms after the game.
"We can't allow that again," Duffy said.
"There cannot be a situation where referees have to walk from the pitch into dressing rooms via an area that is open, that just can't happen again. It wasn't acceptable.
Asked if there would be action taken against the Kildare County Board or where responsibility would lie for the situation, he answered: "First of all, it's our fixture – there's no point me passing the buck to anybody else. It was a Central Council fixture, therefore the responsibility rests with us.
"You can say it was a Kildare venue, but essentially it's a Central Council fixture so the onus is on us to see what happened and make sure it doesn't happen again," he stated.
"I'm not going to blame anybody else.
"What happened on Saturday night was absolutely unacceptable and it's up to us to make sure it doesn't happen again."
He added that the situation was possibly one that should have been foreseen.
"In fairness, maybe we should hold our hands up on that part.
"Conditions on Saturday night were fine, a great atmosphere, I had no problem that end of it.
"You could have said it should have gone to somewhere to get a bigger crowd – everything was fine except that.
"But what happened to us on Saturday underlined that there is an issue in Newbridge and that will have to be addressed before there is a game there again."
He added: "Doesn't mean it can't be used, but that issue with referee safety wasn't acceptable."
After beating Kildare, Tyrone continue their qualifying campaign against Meath in Croke Park tomorrow (7pm), while Donegal attempt to pick themselves up when they face Laois in Carrick-on-Shannon (5pm).