At first blush, the announcement that the city plans to close a 40-bed drug treatment facility on Southampton Street at the end of this month sounded like an outrage.

First, because the program being axed is relatively small, and thus not all that expensive. Second, because it serves a population that has already seen its services interrupted once before — when the city abruptly shuttered the Long Island Shelter a couple of years ago, displacing all who lived there.

Word that the Walsh administration was again failing people in recovery was spread by City Councilor and mayoral aspirant Tito Jackson. He put out a statement branding the decision to close the shelter a “disgrace,’’ and ordered up a City Council hearing.

His statement was light on details, which got me asking questions.

The shelter in question, near Fire Department headquarters in Newmarket Square, provides residents with a bed, a locker, and social services. It was part of the makeshift solution to the Long Island crisis, and is largely funded by the federal government.

Missing from Jackson’s statement was that the US Department of Housing and Urban Development has acted on a two-year threat to pull $800,000 in funding for it. HUD has been pushing cities to place people in permanent housing, and to further that policy it has cut funding for so-called transitional housing. The government maintains that homeless people, including those in recovery, do better outside of shelters and in homes.

Of course, that policy would not justify tossing 40 desperately needy people out on the street. But the Walsh administration maintains that it is doing no such thing. An official for the Department of Neighborhood Development insisted that the city intends to place the Southampton Street residents in permanent housing, and that their treatment services will continue uninterrupted as well.

Clearly, both sides cannot be right. Either the shelter residents are being made homeless again, as Jackson says, or they are not.

Jackson wasn’t backing down Sunday from his contention that the city is failing people in treatment. But when I asked him how he knows there is no plan for the people living on Southampton Street, he said much of his information had come from two residents of the shelter. “When I talk to those brothers and look in their eyes, they’re the people I believe,’’ he told me.

Jackson acknowledged that the administration has told him otherwise, but he brushed aside their assurances. He didn’t present any facts to the contrary. He simply doesn’t believe the administration.

“I listen to the people who are supposed be served,’’ Jackson said. “And I also look at the record of the Boston Public Health Commission, and how they handled the Long Island Bridge [closing]. They have a poor record of planning, and how to help homeless residents and those with addiction issues.’’

Sorry, councilor, but that’s a pretty thin case for declaring that City Hall doesn’t care about homeless people in recovery.

Jackson is right that the closing of the shelter deserves close scrutiny, and that its residents deserve to keep every bit of the support they are now receiving. But if he is going to launch an all-out attack on such a sensitive issue, it’s incumbent on him to have more than just his own suspicions.

Unfortunately, this appears to be part of a troubling pattern. In the course of his campaign, Jackson has claimed that the city has committed $15 million to building a helipad for General Electric. That isn’t true. He has claimed that the restoration of the Northern Avenue Bridge is coming at the expense of Boston Public School students. That isn’t true, either. Jackson claims that the unemployment rate in Roxbury is 17 percent — a figure extrapolated from census data compiled for the years 2010-2014. It’s a guess, not a real number.

Jackson is a talented politician, with a good issue — the growing economic inequality that afflicts our city — on which to build his campaign. But he doesn’t have to grope for examples to make his point. The Walsh administration is as flawed as any other, but it hasn’t been institutionally heartless.

Adrian Walker is a Globe columnist. He can be reached at adrian.walker@globe.com. Follow him on Twitter @Adrian_Walker.