The original request said the system did not allow fractional reserve [banking], and you cannot believe that in light of the evidence that fractional reserve did exist.
You're right, I don't believe fractional reserve banking with bitcoin can exist, and you have yet to provide any evidence to the contrary.
MtGox was operating with a fractional reserve for some time. Either intentionally (criminal) or not (negligent).
So...in your mind, BTC exchanges are operating as fractional reserve banks. That's a rather...um, unique position to hold. I suspect the operators and customers of the exchanges would disagree with you, though.
There is at least one bitcoin "bank" currently offering to pay interest on bitcoin deposits.
Just because businesses are paying interest on bitcoin deposits and/or charging interest on BTC loans does not mean they qualify as fractional reserve banks. But since your definition of fractional reserve banking seems to differ from the generally accepted definition, I guess you can make any claim you want. In any case, it sure would help your argument(s) if you could back them up somehow.