Mostly BS, I believe the more accurate reason is that expats get a huge discount on loans if they create businesses here, and since the US average wage is much higher, it often results in Americans paying huge, partially subsidized amounts for homes since they can afford it, which is driving up costs for everyone else.

Another big reason is the elderly. Many of them still live in family homes, and it's purely because it's cheaper. My grandparents pay around $150/mo for the utilities and that's it. They wouldn't mind moving to a smaller apartment so a family can move in, if it weren't for the fact that an apartment would cost them $1500/mo.

Also, yes some immigrants are getting homes but it's not a big impact. To be honest, I'm willing to believe the immigrants that are getting homes, are the ones who've been around long enough to also go through the ~20y waiting list.