The title is misleading.
First, Jimmy Johnson understood defense and his defensive system. He wanted smaller, faster players. Smaller, faster players aren't exactly found in the top rounds of the draft, particularly for defensive players. Smallish DT and DE aren't considered blue-chippers.
Second, Johnson drafted offense because of where the Cowboys sat in the draft. Troy Aikman was a no-brainer. The Cowboys had to take a franchise quarterback. You need a player who is going to touch the ball on every down on offense. No other player does that. And the cornerstone of your franchise is the quarterback.
Third, Johnson wanted Junior Seau or Cortez Kennedy in the 1990 draft, but we had given up our first round draft pick (that would have been No. 1) to take Steve Walsh in the supplemental draft. Image having Kennedy
AND Emmitt Smith.
Then, again, maybe we don't get Emmitt if we had a first-round pick in that draft.
Fourth, in the 1990 draft, Jimmy wanted either Ray Agnew (DT who went to the Patriots) or James Francis (who went to the Bengals). The Bengals didn't want to deal so the Cowboys stayed put, then when they saw Emmitt dropping they traded with Pittsburgh to nab him. And the rest, they say, is history.
Fifth, in the 1991 draft, the Cowboys picked Russell Maryland overall and followed that pick with Dixon Edwards and Godfrey Myles.
So, in sum, it's not like Johnson didn't value defense. In fact, he did and would have picked defense had the draft fallen right. But because he knew defense, he knew what players fit his scheme. I don't know how one argues that Johnson built the Cowboys without an eye on defense. It just so happens that Aikman and Emmitt were generational players, and I don't care how much you need a defensive player, if you believe a player is a generational talent, you take him, ESPECIALLY when you need a quarterback and a running back.