I don't know what it means to be built to make a lot of pars, but yeah, him not playing the typical birdie fests is of course true. He plays courses which usually doesn't see that low scores. In his better years, he was very high, if not leading the tour in birdies.
That doesn't mean he can't shoot something low. He shot -14 at the PGA and -17 at the BMW last year. If he had played the John Deere or Wyndham and had a good week, I don't see why he shouldn't be shooting 15-20 under.
He didn't get to +4 because he wasn't trying to make birdies, but playing conservatively for par. He just didn't play any better.