Yep, my bad. Thanks for the correction.
However, if our first draft was 2002, why were the players wearing "10 year" badges in 2012? Wouldn't the 2012 season have been our 11th? Or am I remembering the badges incorrectly?
As for how many teams have had the first draft pick in all the drafts since the 2002 year, no other team has had multiple 1/1 picks. The Texans have had 3, if you want to include 2002, two if you don't. The other teams were Chiefs, Fisher 2013; Colts, Luck 2012; Panthers, Newton 2011; Rams, Bradford 2010; Lions, Stafford 2009; Dolphins, Long, 2008; Raiders, Russell 2007, Texans MW 2006; 49'ers, Smith 2005; Chargers, Manning/Rivers 2004; Bengals, Palmer 2003; and Texans again Carr, 2002. And of course the Texans again in 2014 where they picked Clowney.
Call it what you want.