In the latest instalment of perceived injustices in the trans-Tasman cricket rivalry - dating back to the 1981 underarm controversy - New Zealand's only inductees to the Hall of Fame appear as Australian, next to an Australian flag.
Former allrounder and Canterbury representative Hadlee was in the original induction when the Hall was opened in 2009 while long-serving White Ferns captain Hockley was inducted in 2014 and batting great Crowe a year later.
Hadlee told RNZ he wasn't aware of the mistake and hoped it would amended.
"We come from New Zealand, I just hope somebody can correct it, so that's all I'd say on the matter.
"I'm too old to get involved in these sorts of things. People know that Martin, and Debbie and myself are all from New Zealand so it's not an issue for me."
RNZ has sought comment from the ICC.
Elsewhere on the website, a drop-down menu of what should be the nine test cricket nations actually only numbers eight, with New Zealand excluded.
Of the 112 players in the Hall, only Zimbabwe - with one inductee - has less than New Zealand's three.
England has the most with 32, followed by Australia 29 and the West Indies 21.
Allrounder Hockley, 61, broke ground in women's cricket, becoming the first to play 100 ODIs and score 4000 ODI runs.
Crowe, who died in 2016, scored 5444 test runs and was admired globally for his classical batting style.
Crowe is the cousin of actor Russell Crowe, who was born in New Zealand but is often referred to as from Australia, where he has lived most of his life.