This is a fair point. To Wikipedia's credit, I think it's adequately addressed in the article I linked.
I think a more general statement could be made. It's nearly useless to make comparisons between countries. The United States cannot adopt Swedish policies and expect to achieve Swedish outcomes. I'd much prefer we discuss policies for our countries in our own contexts rather than introducing comparisons between them.
The parent comment introduced a comparison, though. So, I think it's only fair to introduce some form of statistics.
Thanks for providing a more founded empirical interpretation of the facts! It seems Sweden has some edge on the USA, but the original claim (that it's almost impossible to be homeless in Sweden) still seems as unfounded as I expected.
As another commentator noted, I think climate is something to consider. I expect that you'll find higher concentrations of shelter-less people in more temperate (or at least warm) places. Cultures will evolve to prevent people from needlessly dying, but we aren't inclined to give more than the bare minimum.