I don't see any data about where people are from in that link. Just where they lived most recently. A good way to become homeless is to move into an unstable housing situation in a far away place with high rents.
"Seventy-one percent (71%) of respondents reported they were living in San Francisco at the time they most
recently became homeless, an increase from 61% in 2013."
It's true, it doesn't measure length of stay, but they came from SF and claiming it's still an external problem with no evidence seems particularly disingenuous.
The original statement "They vast majority of poor in SF grew up there or in nearby areas, they didn't migrate there like the economic elite have." is simply not supported by this evidence.
Given historical population growth of California, I think it's not a winning argument. Very few of California's residents have moral ground to live here at the exclusion of others. Pretty much everyone moved here. The only way forward is to allow enough homes to be built for everyone who wants to live here.
It's true, it doesn't measure length of stay, but they came from SF and claiming it's still an external problem with no evidence seems particularly disingenuous.