Whale Oil publisher Cameron Slater said he received the information from an anonymous "tip line" and had no idea of its source. He had been sent "a whole lot more" information - some of it potentially severely embarrassing - but had not published it as he did not consider it relevant to the workers' criticism of the company.
"They are saying the company is not a good company, but all the evidence says it is a good company."
Mr Slater said it showed the company going out of its way to accommodate both workers in their hours of need.
Council of Trade Unions president Helen Kelly said the information about Mr Walker could only have come from the port company, and she called on its Auckland Council owner to end the "corporate thuggery" it was inflicting on its workforce.
"The law is very balanced to allow businesses to collect all this private information on trust, and then hold it on trust," she said.
"If the port company thinks that when it gets up shit creek because of its own behaviour it can use this information to discredit its workforce, the council has got to step in and control this board - it's out of control."
Port chief executive Tony Gibson would neither confirm nor deny responsibility for the alleged privacy breaches, or comment on what steps would be taken to safeguard other confidential information.
A spokeswoman would say only that he was looking at claims by the Maritime Union, which has lodged a complaint with the company under privacy legislation, and that he would respond to the union in due course.
Neither would Auckland Mayor Len Brown comment, leaving it to a spokesman to say it would be inappropriate to do so.
Mr Walker denied the blog site's claim that he "slagged off" the company during the radio interview, saying he had simply voiced his fears about what its proposal would do to family life.