Another poster asked almost the exact same question, and discussed the flaws in his logic here:
link
What it boils down to is that the (correct) method you used to calculate the odds implicitly takes into account the possibility that opponents hold cards. You are only interested in how many "unseen" cards there are. I discuss the reasons for this in the thread above, and also show how you can explicitly factor the possibility of opponents holding cards -- it just makes the computation much more difficult but arrives at the same answer.
Cheers,
gm