It's interesting to think that money is one of the things that the Internet hasn't "distrupted" yet, but maybe this is one attempt.
Speaking of trust, one should remember that the dollar bill was a promise from the Federal Reserve to pay whoever had that piece of paper to pay them the actual money written on it. I wonder who would trust the Central Bank of Facebook that they're "good for it"?
FYI, as written, that statement makes little sense. The term "actual money" does not mean anything. US dollar notes are actual money.
Before Nixon Shock, the dollars were on a gold standard. The government had a promise to give whoever had the US note the specified amount of physical gold (metal). As it is now, it is called a fiat currency, and no government exchanges it for gold or any other metal or any other form of money. It is still "actual money" though, by most sane definitions.
See China or plenty of other countries where people send money to each other via mobile.