Fact is Jones through Lacewell ran scouting till the 2005 draft when Parcells got him tossed and helped get promoted up two (2) levels Ireland. A guy stuck pretty deep in the scouting organization behind Ciskowski and Lacewell.
So ..... basically it was 2005 when Parcells got MORE say in an area Jones kept him pretty much away from till then. Of course BP had input in 03/04 but he was not allowed to draft he precious 3-4 D guys. That says alot to me.
Let me add MORE does not equal absolute. MORE is bigger than SOME. Parcells had SOME say before 2005 and much MORE afterwards. He got his boys in 2005 ......... he got his power ..... he made sure the coffee was hot and tasty at Valley Ranch.
I can even go pull articles with Jones saying as much -- Parcells was hired to coach, not GM. 2003 went well. 2004 poorly. By 2005 he was playing GM and Coach cuz Jones let him remake the organzation in a Tuna kind a way.
But if I had to speculate on who Parcells wanted from 2003 and 2004 -- the two OL come to mind. The rest I can see Jones type thinking. 2005 and 2006 all BP.