you are interacting with the chronic permanently homeless population, what gp is talking about is the fact that there is an even larger population of temporarily homeless. although the statement is true, i don't think it is a useful distinction, because what most people mean by 'homeless' is those chronic cases, anyway, and that is the problem society, government and homeless charities are trying to solve. acknowledging there is another set of people with similar problems is great, but as pointed out, these people generally are getting the support they need, and are a 'solved' problem (in some sense) unlike the people you have been interacting with, who still need some kind of help and are not receiving it...

the skepticism is justified by simply defining homelessness as being without a home for more than a few weeks (the 'usual' definition, tbh) thus making gp's statement obviously false, i suppose.