Sure, the burden is on them to make this real, but not for them to prove it to _you_.
If they want to prove to the chronically homeless that they can get a home, they only need to follow through with the home.
Or perhaps they want to prove to their constituents that the number of chronically homeless has diminished. Easy enough: tell their constituents where to go to count homeless people. Again, it's not incumbent upon them to count, or even to provide easy access to the location. Just give verifiable steps and expect your constituents to do some legwork. (Most won't, but maybe a news crew will.)
If they want to prove to the chronically homeless that they can get a home, they only need to follow through with the home.
Or perhaps they want to prove to their constituents that the number of chronically homeless has diminished. Easy enough: tell their constituents where to go to count homeless people. Again, it's not incumbent upon them to count, or even to provide easy access to the location. Just give verifiable steps and expect your constituents to do some legwork. (Most won't, but maybe a news crew will.)