Mayor de Blasio committed $500 million to Metro-IAF’s plan for building new apartments for seniors, starting with six already identified NYCHA and Housing Preservation and Development sites where money could be spent and units put up quickly. Or at least that’s what the community group says.

And what Council Speaker Corey Johnson says, and Controller Scott Stringer. And headlines like “City says it will spend $500M on new housing for seniors.”

As rents and homelessness keep hitting record highs here, it’s what everyone seems to have heard de Blasio say when he shook hands with Rev. David Brawley of Metro-IAF’s East Brooklyn Congregations on the steps of City Hall last June. The mayor called the new money an investment in “fairness,” so “people who worked so hard their whole lives can actually make ends meet.”

Now, City Hall says that, actually, the mayor meant about $100 million from the city, with the feds and other development partners bringing in the rest. And that this was always clear, and that they’re confused how people ended up with $400 million worth of the wrong impression about the commitment de Blasio made.

It reminds me of a classic Daily News front page: “He Said-She Said, She Said, She Said, She Said, She Said, She Said, She Said, She Said, She Said,” and on and on, from the press and the pastors and the other politicians and the public. (If he doesn’t recognize the reference, de Blasio could ask his old political pal Louis CK.)

Back to Metro-IAF, they have a high-pressure approach: insisting politicians first to respond to the group, then to meet with its members, then to publicly commit to the group’s goals, and finally holding the politicians to account for those commitments.

The group has every reason to play things straight, since they don’t have billions of their own, or lobbyists. Their currency is their word and their proven ability to live up to it. And de Blasio?

“I don’t feel good when I see something that’s someone quoting someone, so we’ll put out a clear statement about this,” he said Monday, after Errol Louis asked on “Inside City Hall” about a Daily News editorial questioning the city’s reported plans for less than 1,000 units on those six initial sites. “Some of the advocates involved had ideas that although I’m sure noble were not necessarily functional.” De Blasio then asked himself: “But the notion of creating more senior affordable housing?”

He answered himself: “Absolutely a high priority. And I think this idea can work — we have to work out the best way to do it.” Council officials, though, say that they’ve had a hard time extracting basic information over months of frustrating meetings with administration officials. City Hall spokesperson Jane Meyer says a response is coming soon to a letter from the controller’s office demanding specific updates about the money dedicated to the initial sites the city identified and the progress of the apartments there.

“We are following through on our commitment and moving aggressively to get these six sites totaling $500 million in development costs built,” Meyer emailed Friday. “We have already financed over 7,000 homes for seniors, and we all must all work together to provide more.” Speaking of clear statements, “there was no ambiguity from the mayor when we shook hands about this being $500 million from the city,” Brawley told me Friday.

“If in fact we have been deceived and lied to, this would be a great disrespect to the black and Latino community — certainly the greatest lie that I have ever seen, and maybe in the history of our organization.”