You're making an apples and oranges comparison. In the fall of 1996, when Brees would have been recruited, Mencke and Birnbaum were young guys (freshman and redshirt freshman respectively) playing behind arguably the greatest sophomore QB in WSU history but on a team that was struggling. As a result, Birnbaum only threw 20 passes in the entire 1996 season. There was no way to know in that season what was going to happen in 1998. As mentioned above, Birnbaum was a big, strong kid in 1996 who looked like he had a bright future. Here's a listing of the QB's that Price had on his roster from 1996 to 1998:
1995 - Ryan Leaf - 6' 5"
1995 - Steven Birnbaum - 6' 5"
1996 - Paul Mencke - 6' 5"
1997 - Dave Muir - 6' 5" (transfer or walkon?)
1998 JC transfer Bryan Paul - 6' 3"
Drew Brees was 6' 0". Yeah, Price screwed up when he didn't offer him, but it's pretty obvious that Mike was infatuated with tall, pro style QB's at the time and wasn't going to give a runt like Brees the time of day. At the time he would have been recruiting Brees, there was nothing to suggest that he should assume that Leaf wouldn't be there in 1998 and that Birnbaum and Mencke would both have an extra year to get ready. Given the number of young guys on the roster, it's no surprise at all that Price passed on Brees.
Compare that with today's situation where we have a pair of seniors on the roster that "need the competition". FWIW, I get the concern that everyone has with Tinsley and Gordon and I wish that I felt more confident in them. I get the desire to find an extra body, but y'all are just lying to yourselves about the situation when you say that this situation is anything like recruiting Brees in the fall of 1996.