That may not be necessarily true. Rates are not higher for immigrants, whether they are permanent resident aliens or have allowable visa's.
Of course, if you have cash, that always works. If you're hoping to get a loan, there are several options. Different Visa's can be used to obtain conventional or government loans. Same with a permanent resident alien.
You can also actually obtain a permanent visa by buying real estate, believe it or not. It's called an EB-5 Visa. There's different ways to leverage this, but an EB-5 visa is a visa given to a foreign national because they invested in US real estate. There are different provisions for an EB-5 Visa, but the typical guidelines (different if applied through a Regional Center) require an investment of $1,000.000 in US real estate and the property must produce jobs in the US. There's also specific regions that only qualify. The visa is a permanent one though, so you can begin working on getting your permanent green card after you obtain it.