Sixteen of Brandon Phillips' RBI came immediately after a Joey Votto walk. Now let's look at times when Brandon Phillips has driven in Joey Votto himself:
Yep, that's right, four of the seven times Phillips has driven in Votto, it's been after a Votto walk. Twenty of his RBI have been of Zack Cozart and Shin-Soo Choo. Let's see what Votto did immediately before those RBI:
Votto is advancing the runners ahead of him when he bats, even on his walks. So why isn't Joey Votto driving in Choo and Cozart as often as Phillips is? Because Votto doesn't have Votto batting in front of him to advance those runners.
It's silly to compare RBI totals of hitters who bat behind each other in the same lineup, as one isn't independent of the other. And it's silly to treat driving in runners as a binary choice (either up or down). You can advance the runners ahead of you. You can simply avoid making outs and keep the inning alive longer for the batters behind you. You can provide baserunners yourself. Votto is doing those things, and it's making Phillips' RBI totals look better.
The other thing to note about Votto is that in order to walk, you need to see four pitches outside of the strike zone. In order to walk less, he'd have to swing at more pitches in plate appearances where he saw mostly balls. The whole reason they're balls is because they're not good pitches to hit—that's why the strike zone is where it is, to define the pitches that are good to hit. So in order to walk less, he'd have to start swinging at more bad pitches. And if he starts swinging at more bad pitches, pitchers are more likely to throw him bad pitches. It's not like he can make the pitcher forget that he's pitching to one of the best hitters in the National League and force him to throw the same number of strikes he throws to every other hitter.
I could be silly and propose something like the "sacrifice walk" where a batter refuses to swing at bad pitches to pad his RBI totals and instead sacrifices his at-bat to keep the inning going and give the batters after him a chance to drive in those runners, but I'm afraid someone would take me seriously. Instead, I just want to note that run scoring is a team effort, and the reason we savants have such low regard for the RBI is that it doesn't do a good job of recognizing the totality of a hitter's contributions to his team's run scoring, focusing on runners driven in to the exclusion of things like runners advanced and out avoidance. Joey Votto's bat is more valuable to the Reds than Brandon Phillips', and if you find a metric that says otherwise, the trouble isn't with Votto, but with the metric.