Assuming that Facebook is the sole issuer and redeemer of the coin, this is a nonissue. By backing the issued coin 1:1 with reserves according to the composition of the basket, Facebook can redeem any coins at face value. Hong Kong, for example, maintains a currency pegged to USD backed entirely with USD holdings.
As an aside, your source, armstrongeconomics.com, may not have the best credibility:
"In 1999, Japanese fraud investigators accused Armstrong of collecting money from Japanese investors, improperly commingling these funds with funds from other investors, and using the fresh money to cover losses he had incurred while trading. United States prosecutors called it a three-billion-dollar Ponzi scheme... Armstrong admitted to deceiving corporate investors and improperly commingling client funds—actions that according to prosecutors resulted in commodities losses of more than seven hundred million dollars—and was sentenced to five years in prison."
In the context of Facebook being pegged to a basket of international currencies, the peg to each will need to be reevaluated frequently as the currencies fluctuate and arbitrage opportunities increasingly cost the peg-guarantor money to uphold the peg. These fluctuation can be cancelled by derivative contracts e.g. currency swaps, but those cost premiums to maintain and periods of volatility can get very expensive.
[1] https://www.google.com/search?q=site%3Aarmstrongeconomics.co...