On Friday, Eiding said the PHA board structure was like no other board he has served on, without committees or a typical oversight role. That left Greene - and perhaps others, Eiding said - an opening to keep settlements hidden for at least four harassment claims between 2004 and the present.
"It's unique in a lot of ways, and it gives an awful lot of leeway for the professionals hired by the authority not to be as professional," Eiding said.
In retrospect, he said, he would have demanded more accountability from Greene and PHA staff.
"If I have some fault at the end of the day, that's fine, I'll stand up and take it," said Eiding. "I guess I acquiesced to the belief that if professionals see something wrong, they're going to let us know."
As recently as Wednesday, Butkovitz said he planned to reappoint Eiding when his five-year term expired next month, despite the controller's own public criticism of his appointee for missing six of 15 meetings between February 2009 and June.
But on Friday, Butkovitz was noncommittal.
"I've got to think about this whole governance thing," Butkovitz said. "I wouldn't say it's lack of confidence, it's that matters at the PHA are going into a new phase, involving very intense type of oversight.
"I would say there's a crisis at PHA right now."
Nutter called Blackwell "a champion in terms of her advocacy and making improvements in the community."
But Nutter also said this week: "If this were a board or commission of the city ... I would certainly be handling this matter in a very different way than is going on right now."
Nutter spoke Wednesday about her seat, which has been up for reappointment for nearly two years.
"She is quite well aware that this is a matter that I am actively evaluating and looking at, all in the context of the issues that are swirling around the board," Nutter said Thursday. "I'll be talking with her about that and making a decision relatively soon."
Nutter is hamstrung on his other appointment until September 2011. That's because board Chairman John F. Street reappointed himself to the board in May 2007, his last year in office. Nutter criticized Street for breaking what he called a "time-honored tradition" of letting an incoming mayor control appointments in his or her term.
Blackwell was raised in public housing, and her dedication to housing issues is well known. She continues to be the chief defender of Greene, whom she calls "a genius."
Blackwell was originally appointed in May 2002 to replace former Mayor Edward G. Rendell's unexpired term, which was ending in September 2003.
Her reappointment to a five-year term took her to September 2008. Nutter said he was never notified by Street that Blackwell's appointment was expiring, as required by the PHA board's bylaws. Street declined to comment.
The maverick councilwoman - more of an ally to Street than to Nutter, but always unpredictable - said she told Nutter on several occasions early in his term that she wanted to stay on the board.
"It's my life. It's what I do. It's what I believe in," she said. "It's who I am."
The state law governing the PHA allows members to continue to serve beyond their appointment "until his successor has been appointed."
Nutter and Butkovitz have two appointees each; the fifth is elected by the other four.
That member, Nellie Reynolds, also is serving a term that expired in April, according to documents released Friday by PHA.
Butkovitz reappointed his other pick, Debra Brady, in January. Brady, who runs Philadelphia Writ Service Inc. and is the wife of U.S. Rep. Bob Brady (D., Pa.), the city's Democratic Party chairman, missed 11 of the 15 board meetings between February 2009 and June.
Butkovitz reappointed her in January, and her term runs through 2014.
Eiding, who said his busy union schedule sometimes caused him to miss meetings, particularly if they were rescheduled, said he deserved to be on the board. He took issue with Butkovitz's criticizing his attendance in the media. Union members perform virtually all of PHA's construction and maintenance work.
"I'm very disappointed about his comments," Eiding said. "Certainly, I take those positions very seriously, and if he feels that I can't carry out the responsibility of the job in his evaluation, then he has to make a decision.
"I think I deserve the reappointment. Whether I want it or not has to be a discussion between me and the controller."
Contact staff writer Jeff Shields at 215-854-4565 or jshields@phillynews.com.