Nicholas is right. Everyone is making this more complicated than it has to be.
Your parents, US Citizen, foreign nationals, whatever... does not matter. They can simply gift the funds to you for the downpayment, as long as 5% of the downpayment comes from your own pocket. That's it...
At Wells Fargo, as long as the funds are gifted prior to the application, then we just need the gift letter. If the gifts were given after the start of the application, then we need a letter from the bank that the funds come from and documentations that the funds were transferred into your account. Of course, every bank does it a little different.
Hope that helps!