Taking someone as an intern is an effort for a company. Of course you can build something very useful, but you will need to be given a lot of company's resources like a lot of money and time of people like your intern manager, recruiters etc. They teach you a lot to make you a better programmer. That is profittable mainly in case if you will return to that company as a full-time employee. However in order to work in USA you will need a work permit which boils down to obtaining H1B or L1 visa. First one is based on a lottery. Many people apply and constant number of visas is given to random people who applied. With each year number of people applying is growing significantly and number of given visas is constant, so the probability of getting visa is getting smaller every year. Last year that probability rapidly dropped (approximately from 50% to 25%), so only one in four engineers who Facebook wanted to hire were given a work permit, hence it became a lot less profittable to invest a lot of resources into interns from outside of US. L1 visa is "transfer within a company". If you work at company X for at least one year then you can be given work permit in that company in US (note that you can't change company). However Facebook's software engineers offices outside US are small and FB is very reluctant to hire people there (it's not that easy as it seems to make an office bigger), so getting that type of visa is also hard.

You can definitely try applying to US offices of different companies. In case you won't get visa in a future then you can work in their offices outside US (and maybe after a year get L1 visa), it's just FB's case that they have little work positions outisde US.