I usually refer to WAR myself most of the time when I want to get a quick surface evaluation of a player and how "valuable" (very arbitrary). But I think there are real limitations that I think need to be acknowledged. For example, two years ago Dan Uggla was rated as a plus defender and subsequently had a WAR of 3.3. However, there are mountains of evidence that suggest he is otherwise a very poor defender which inflated his total quite substantially. I think public defensive data is fine in the aggregate but individual samples of player data can be misleading.
My point in the end is that I think it's fine to use it as a pretty effective rough estimate, but I also feel like it is imprecise enough to question in individual cases when there is a logical reason. For a player like Markakis, thats extremely important since his WAR is pretty dependent on his perceived range. We just don't have the slightest idea about how defensive performance is year over year. Even markakis, he was an exceptional defender based off the metrics for the first 4 seasons of his career and then the next year he cratered and he's been bad ever since, without major injury. It's just a weird phenomenon.