Speaking at a Currie Cup function in South Africa, he responded to claims New Zealand's postponement from its third Test with Australia, the second game of the Fortinet Rugby Championship, had fractured the Sanzaar relationship.
This was after South Africa had been unable to play in last year's Rugby Championship as a result of the Covid-19 pandemic.
Last week's decision by New Zealand, as a result of a lockdown due to an outbreak of the Delta variety of Covid, fired another round of media comment in South Africa that the world champions should look to breaking into the Six Nations tournament in the future.
But Alexander said there was no rift between the Sanzaar members.
"We don't take every argument as a rift. We have bigger battles that we fight in the boardroom," he said.
"We have local arguments here, but that doesn't mean we're fighting each other. It's like when we have a meeting. We fight like hell in the boardroom, but when the door is open, the fight is over.
"I don't think we should read too much into these things, and the media plays things up and blow things out of proportion.
"There isn't a fight within the Sanzaar structures," he said.
In the championship, the All Blacks and South Africa will play their 100th Test on September 25 in Townsville.
They play their second-round game against Australia in Perth on the weekend of September 3-5. Then they meet Argentina on Sunday, September 12, on the Gold Coast and, six days later, they play Argentina again at Suncorp Stadium.
The second game with South Africa will be played on the Gold Coast on October 2.