It means either there was a faulty test or someone is not being honest - either about having the FVL mutation or about your parents...You have to have inherited a mutated gene from your mom or your dad (if you're hetero. If you have 2 genes, homozygous, then BOTH your mother and father HAVE to have at least one mutated gene to have passed on to you). As far as I know, FVL does not "skip" generations. So unless you've always suspected you're adopted, your father is not your "blood" father, or the hospital mistakenly switched you at birth, it had to have been an faulty test - either your positive result is wrong or their negative one is.
It is entirely possible for you to be the only sibling to inherit the disorder, but one of your parents has got to have the gene.

I have tested positive, father, mother and only sibling have tested negative. Is it possible to have this condition due to blood transfusions?

If your parents have been checked at least twice for FVL then I would suggest you get tested again.

Not true...although unlikely it is possible for you to have developed the mutation without either parent having it. This is my case, we have gone through multiple Factor V testing all of us, and paternity testing. So it is possible for a child to have it without either parent having it. In my case I have the heterozygeous verison.