"I don't think it is the big three any more," Parish said.
"I actually think it is the big six or the big seven because they have changed the international eligibility rules for players and I think the gap between the third and fourth, fifth, sixth and seventh nations isn't that great now."
While Scotland secured a draw with New Zealand during last year's Four Nations and Italy shocked England in a warm-up match before the 2013 World Cup, no tier two country has beaten one of the big three in a Test or major tournament for more than 35 years.
However, Parish said the new eligibility rules would enable the likes of Samoa, Tonga, Fiji and Papua New Guinea to field their strongest possible teams for the first time during this year's World Cup in Australia, New Zealand and PNG.
"Everyone wants to see the best players playing and that is what is going to happen in this World Cup, which is fantastic," Parish said.
One of those players is Brisbane five-eighth Anthony Milford, who is set to play for Samoa for the first time since the 2013 World Cup in the May 6 Test against England at Campbelltown Stadium.
Previously Milford had been unable to play for Samoa and remain available for State of Origin selection with Queensland but under the new international eligibility rules players can nominate a tier one and tier two country they wish to represent provided they qualify for both.
Therefore, if Milford or forwards Josh McGuire and Josh Papalii are not chosen by Australia for next month's trans-Tasman Test or the end of season World Cup they can play for Samoa.
"One or two really good players can make a great difference to your team," Parish said.
"You look at someone like Anthony Milford, who was a standout in the 2013 World Cup. Before that he had only played like nine NRL games for Canberra.
"He has kicked on since then but the unfortunate thing about that is that Anthony hasn't been able to play a Test for Samoa and nor has he played an Origin game or a Test for Australia.
"He wants to play for Samoa and everyone wants to see him play for Samoa but up until now it hasn’t been able to happen.
"None of us want to stand in their way of guys playing Origin, or for Australia or New Zealand, if they can do it but if they can't and they have got the heritage they should be able to play for other nations. That is going to happen now and it is really exciting."
The change to the international eligibility rules also create a greater depth of talent for the Pacific nations and Parish said there would be genuine competition for places in the Samoa squad, which will be led by senior players Frank Pritchard, Sia Soliola and Antonio Winterstein.
"People talk about the international game not being as competitive as some other sports, well I can assure everyone now that this World Cup will be competitive," Parish said.
"While Australia, England and New Zealand have been the standouts in rugby league for a long, long time I have got no doubt that one of the other nations can beat one of those teams in this World Cup, which will be exciting for everyone."
Samoa is drawn to play New Zealand at Mt Smart Stadium on October 28 before meeting Tonga in Hamilton on November 4 and Scotland in Cairns on November 11.
"They are all big games so we are going to need all of our players," Parish said.
"Guys like Frank Pritchard, SIa Soliola and Antonio Winterstein are not only good players but they certainly drive the standards of what you want to achieve on and off the field and I am really looking forward to working with those guys.
"This Test in May is a massive part of our program for the year and what we want to do for the World Cup.
"There has been a lot of planning for the World Cup around training venues and hotels and getting programs all set so it is all pretty exciting and it will come around quick."
This article first appeared on rlwc2017.com