I don't really see a problem of fractional reserve happened to bitcoin. For it to work, you need to trust that the IOU's issued by the fractional reserve, and we see more and more people have stopped putting faith into other people/companies/exchanges.
The problem with exchanges/services running on a fractional reserve system is that there is a risk that the person running the exchange/service is going to take on too much risk that results in them having negative equity along with the fact that there is a risk that there will be a "run on the bank" that results in more withdrawal requests then the amount of bitcoin the exchange/service has/controls