While I bear zero animus towards immigrants, this seems obtuse. Why are those companies willing to pay so much? Because they predict they can charge enough rent to make it profitable anyway. Why would they think that? Because immigrants can compete down at the level of rents.
This seems like the same mistake people make about "luxury housing," but on the other end of the market. Building housing at the top of the market does indeed make things cheaper at the bottom of the market, and bringing in people at the bottom of the market does indeed make things more expensive at the top.