I have not watched the ABC News shows again, but while reading a NYT article they mentioned the annual count. Looks like they do count the sheltered:
The way that the United States estimates rates of homelessness — with groups of volunteers
counting people who are unsheltered
and in shelters on a few nights every January — ensures that official numbers reflect only the most extreme and visible aspects of the problem. The count of 582,462 people in the most recent report to Congress leaves out, for example, the person finding sanctuary for a few nights on a cousin’s couch. We know that more than
a million people experience some form of homelessness every year. Many of them — 28 percent of those counted in 2022 — are part of families with at least one child under 18. While about a third are chronically homeless, having lived for more than 12 months with a disability and without housing, most manage to get back into housing within a few months. But as you’ll see in their stories, their experiences of homelessness and housing insecurity often continue to affect their lives years after their housing has stabilized.
More:
https://www.nytimes.com/2023/02/10/headway/what-dont-you-know-about-homelessness.html