After winning his opening singles match, Statham produced one of the best performances of his career to beat Pablo Cuevas, the former world No 19, who has six ATP singles titles.
That display was another chapter in Statham's enduring Davis Cup legacy, where he has played more ties (33) and won more singles matches (28) than any other Kiwi, since his debut as a 17-year-old in 2005.
Statham is ranked world No 533, after injury issues over the last few years. But he won't be in Finland, with singles rookies Ajeet Rai (world No 811) , Kiranpal Pannu (759) and Isaac Becroft (997) enlisted alongside the experienced doubles combination of Michael Venus and Artem Sitak.
Tennis New Zealand chief executive Julie Patterson said Statham was originally chosen, before ultimately making himself unavailable.
"He was selected but we couldn't come to terms with regards to the contract so he declined," Patterson told the Weekend Herald.
Patterson said they had talks with Statham "over a period" before he decided to withdraw.
However, Statham's long-time coach Gary Swinkels said his charge is disillusioned and dejected over the episode.
"It's a terrible situation," Swinkels told the Herald. "Any country would be dying to get their number one player involved. He loves playing for New Zealand but it feels like they are not invested in the team doing their best."
According to Swinkels, Statham proposed a preparation plan leading into the tie.
"He wanted to take KP and Ajeet with him, do two or three tournaments beforehand, to get them sharp for the Davis Cup tie and Tennis New Zealand didn't want a bar of it," said Swinkels. "They were not interested.
"Rubin puts a lot into Davis Cup, he puts a lot of emphasis into preparing.
"He is quite unhappy about the whole thing; he doesn't feel he is being treated that well. It is all quite disrespectful and unprofessional."
Swinkels said Statham wanted TNZ to contribute financially to the preparation phase, as well as an understanding about what the build-up would entail.
Patterson disagreed.
"We did consider it but we needed the players that had been selected and had signed the contract before we knew the plan," said Patterson. "We wanted to try and gather as many of the players together as possible, in a place that was going to work for the majority. An individual coming out with their own plan isn't necessary going to meet the needs of everybody else."
Swinkels also feels that the relationship between Statham and TNZ high performance boss Christophe Lambert is strained.
"Everything is personal with the negotiations, it is not business-like," said Swinkels. "This stuff weighs heavily on his mind, the way they communicate with him. He is the No 1 guy in the team and is treated like a 14-year-old."
Patterson didn't want to comment on that relationship but emphasised that there is a clear process and structure around Davis Cup selection that was agreed with all players, including Statham, last year.
"When we have someone that sits outside that team approach, it becomes quite challenging," said Patterson.
Statham declined to comment when contacted by the Herald but said he was sad to be missing the tie.
Patterson agreed it was unfortunate situation.
"I was really disappointed that we weren't able to come to an agreement and I shared that with Rubin as well," said Patterson. "But the situation is as it is and Rubin made his decision from there.
"The upside is that we get an opportunity to see some of our young players. But it wasn't how we had hoped the contract negotiation would end but that's what happened and we have to move on."
Patterson added that the door remains open for Statham in the future.
"Of course, we still want Rubin to play," said Patterson. "He was selected in this team."
Rai (23) has played four singles matches for New Zealand, with his solitary win coming in a tie against Indonesia in 2019. Pannu (25) and Becroft (21) have yet to play Davis Cup.
Finland will be difficult opponents.
Their top singles exponent Emil Ruusuvuori is ranked world No 44, with Otto Virtanen at No 249. They pushed Belgium in March, eventually losing 3-2 as former world No 7 David Goffin came to the fore.