I think there are a couple different issues at work. First is the idea of pitching to contact, versus refusing to give in. It's a trade-off between extra-base hits and walks. I'm not sure one approach is necessarily better than the other... it just depends on the pitcher and the team around him.
The second and more important issue is pitcher quality. If a guy stinks there is no approach that will yield great results. A guy with good stuff can attack the zone and be effective. I think the main reason the Twins lack pitchers with good stuff is their drafting strategy- even after the first few rounds they strongly prefer low-ceiling college guys to raw high schoolers. If you draft enough 18-year olds with a live fastball, some of them will turn into Major League power pitchers.
They have obviously drafted high school pitchers over the years, and had disappointments, injuries, etc., but not to the same degree as a lot of clubs. I understand focusing on college pitchers in the first 2 rounds or so, but after that it's really hard to find guys with much upside. Why bother drafting someone with 5th-starter upside? They can get that anywhere. Take a high school pitcher and work with him. Most will flame out but some will add velocity and learn how to pitch.