That is extremely implausible. What fraction of them would be able to put together the $1000/month (in the scenario of extreme home buildout)?

It's only true in the trivial, unhelpful sense of "if we got housing costs down to $10/month or free, then all the people there could afford a place." But when we talk about housing costs in general and policy around it, we mean something like getting rents down from $3000/month to $1000/month (from vast expansion of building), not some artificial number that no amount of expansion would (scalably) get.

And I don't think you can really take one homeless person living at an encampment, making a self-serving statement, as a source.