Every couple of years, for one game, Mariano Rivera is not cut out to be a closer. He hasn't allowed three runs in an appearance since June of 2009, although he's allowed two runs in a third of an inning several times since.
He's Mariano Rivera. For everybody else, it happens more frequently. Jose Valverde, a not-quite-top-tier closer in the grand tradition of Jason Isringhausen, allows more than two runs a couple of times a year. In 2008 he allowed six runs in a third of an inning against the Pittsburgh Pirates—this was the year after he led baseball with 47 saves, and in the middle of a year in which he led the National League with 44.
Trevor Hoffman, to date the all-time saves leader among guys named Trevor, allowed four runs in 0-1 inning nine times while he was Future All-Time Saves Leader Trevor Hoffman, and not Brewers Trevor Hoffman. That doesn't sound like a lot, but he looked terrible in every one of them.
All this is to say that trying to use one outing—even one catastrophically bad outing—to decide whether a pitcher has a Closer's Mentality, as I saw it put on Twitter, is ridiculous. Even Mariano Rivera took a back-breaking World Series loss; even Trevor Hoffman allowed four earned runs one time out of a hundred.
Mitchell Boggs isn't a closer, and probably shouldn't be one, but it's not a character flaw on his part—it doesn't even show up in the other meaningless stats people use to divine character flaws. (Last year he faced 53 batters with the score tied and allowed eight singles, eight walks, and nothing else.)
He's just not a great reliever, and "closer" is a role that almost by accident tends to accumulate the greatest relievers. His fastball is about three strikeouts per nine innings less impressive than it looks, and last year's dominant season depended on a BAbip of .200 in those same tie-ballgame situations. When Fernando Salas was pitching well, he looked enough like a closer to lead the team in saves. If Trevor Rosenthal looks more like a closer now, it's probably because he's spent his limited time in relief looking like a better pitcher than Mitchell Boggs has.
Sometimes this feels like an overfine distinction to make, but a team's bullpen problems only become more complicated when they're trying to solve a problem—is the pitcher we're bringing in in high leverage situations our best pitcher?—by way of another problem—why is this pitcher we're bringing in in high leverage situations not our best pitcher?
But if it's any consolation, Eduardo Sanchez threw a scoreless inning in Memphis last night.