and the solution is "let facebook be your central bank and currency supplier"?

Indeedy. My country has 7% inflation. And that calculation is done by the very state that is responsible for inflation so their word on this only means so much. Any other currency or store of value that solves this is more than welcome.

Would it be a solution for you to buy foreign currencies with lower inflation amount (e.g. EUR)?

"capital controls" generally includes foreign exchange controls, i.e. restrictions on conversion to foreign currency and local use of foreign currency.

https://en.wikipedia.org/wiki/Foreign_exchange_controls

And why should this be different for a private currency controlled by facebook?

It shouldn't. All capital control is terrible. It could be different though.

A lot of wealthy people do that. It isn't as straight forward though. It would be nice to be able to do so on the internet and for smaller amounts.

Because obviously an instrument backed by foreign currencies will be the solution to capital controls?!