Nope. You're doing the math wrong AND you're casting a very wide net.
First off, if you're looking at the "top 20" rated passers this year, you're going to be including players that a lot of us wouldn't be happy with. Also, are you looking yardage or passer rating or QBR or what?
If you're looking at Yards, then Fitzy is 25th right now even though he's missed several games and if you'd looked a week or two ago, you'd have been including him in your search.
Secondly, when you're looking at those players and seeing that 6 of the top 20 were drafted in the first round, you're not looking at how many players were drafted in the first round to get those 6 players.
I'm going to assume that Peyton Manning is the oldest of these QBs and I'll just go back to 1998. Since 1998, there have been 48 QBs taken in the first round. Of those, only 6 have survived to 2014 and are in the top 20 in passing.
That's 32 whiffs and a 12.5% chance of success and about 2.8 QBs selected in the first round every year.
And when you think about 1st round draft picks at QB, they are given every opportunity to prove themselves; they are carefully groomed and developed; they're given more chances. QBs in later rounds are more-or-less thrown against the wall to see if they stick.
So just taking a QB in the 1st round because the 1st round is more represented in a top yardage list only gives you a 12.5% chance of getting the right guy.