Partly Facetious : What does 'on condition of anonymity' constitute?

"But you know he is kind of lazy and..."
"How dare you! You know that the civilian and the military establishment are on the same page on this man and..."
"Calm down, I am not saying he is not qualified, all I am saying is that he is lazy, and I am not saying it - everyone around him is saying it."
"Everyone around him is saying it on condition of anonymity I presume. I ask you how can you lend credence to someone who doesn't have the backbone to openly acknowledge what he/she told you about this guy?"
"Perhaps after the amendment to the National Accountability Bureau (NAB) law these bureaucrats may be more open."
"Don't be facetious, NAB can only put them behind bars before a conviction, the government of the day can derail their careers and send them to the boondocks so between the government and NAB I would be more scared of the former."
"Well, let's say both have a role to play in their fear - anyway the gentleman's laziness is well documented in the Ministry he runs and his underlings told me that he was too lazy to attend the Asia Pacific Group meeting himself, a subject in the domain of his ministry and not, ha, ha, ha, under the domain of the autonomous State Bank of Pakistan. For the first time ever, a Governor of SBP led the mission to AGP and..."
"Look you know the minister likes to play the top dog, you have attended his press conferences where he is flanked by his lieutenants - Shabbar Zaidi and Hammad Azhar though mind these two men have major responsibilities and are working hard..."
"You know this is all Zardari sahib's fault. I urge the government and NAB to initiate yet another case against our former President..."
"Where does Zardari sahib come in?"
"He promised the top position, caretaker prime minister, got the minister to resign as a senator, and then never delivered. Had he got that position he wouldn't have wanted to be top dog..."
"Don't be facetious, I reckon he wants deniability so the moment something doesn't go as planned he can deny responsibility and put the blame on......"