There is nothing in that analysis that suggests that the reductions aren't real. Quoting in "The Data" portion:
> Figure 2 shows that, measured by its point-in-time counts, Utah experienced a less dramatic, but still impressive 71 percent decrease in chronic homelessness since 2005. Yet should we trust even the point-in-time counts?
Yes. If you want to challenge them, go out and do point in time counts rather than suggest that someone is lying. In fact, challenging them in the manner that the writer is is fundamentally dishonest, suggesting again that research by its very nature shouldn't be trusted.
> In fact, as Figure 3 shows, there were major drop-offs in chronic homelessness during two separate periods: 2009–10 and 2014–15. If not for these two periods, chronic homelessness in Utah would have increased over the past decade.
Just because reductions appear during specific time periods during a research period does nothing to deny the fact that overall reductions occurred. This is like suggesting that a small uptick in violent crime means that crime hasn't reduced at all over the last several decades.
The entire article is anti-science, as the AEI all too often is. If you want to challenge research, you don't do it by suggesting someone is lying, you do it by using the scientific method. AEI really doesn't do any of that, it is primarily there to challenge research to protect support for conservative ideals while making them seem as if they are well researched.