Im not sure about the law in the USA, but in Germany I would beg to differ. Here, if you run a service, you do NOT have the right to arbitrarily reject users. The bigger your userbase is, the less you have that right. So as long as the developer acts within the law, he could demand access to Facebook.
US courts have been very liberal in their interpretation of the CFAA. I strongly disagree with it, and I believe it is downright dangerous, but this is the current legal environment in the US. Perhaps he should move to Germany. Stuff like this probably wouldn't happen there either:
Capitalism is not a force of nature. Countries have an enormous amount of legislation in place to ensure companies can do business, and invest huge amounts of money in services supporting the private sector (infrastructure, education, etc).
These companies wield a tremendous amount of social power, especially services like Facebook. There's nothing odd about holding these companies to certain standards and laws that ensure they can not negatively influence the civil society from which they profit so much. Being allowed to refuse service to the very people that enable your business to exist is a privilege, not a right, and it comes with restrictions.
This is quite normal in most countries outside the US.
See Civil Rights Act of 1964. Many of the act's opponents were dyed-in-the-wool racists and bigots, and the rest of us can be glad that they lost. But there were some others who opposed the act because they understood that a slippery slope was being created.
Those are the limits most people are familiar with. They're reasonable and expected but even in the US businesses have 'the right to refuse service to anyone.' They work in the same way that you can fire someone, but you can't fire someone for being black, or a woman.
The OP claimed that that did not exist at all in Germany.
It certainly is illegal in France.
Refusing to sell without a valid reason is an exception to contract liberty since the sixties (article L. 122-1 du code de la consommation). The former situation was seen as biased in favor of the sellers.
Whether alleged violation of the user term is a valid reason is open to questions. Without going to court, I strongly doubt it is.