Putting Ubaldo Jimenez in the game in that situation would be like a Nationals manager putting Gio Gonzalez into the game in a similar situation. Every team probably has a pitcher who is 50% or more likely to not be able to "handle the moment" and it is unfathomable to actually put that player in before it's like the 19th inning and he's the only one left in the bullpen.
In addition to Britton, they also had Tommy Hunter and Dylan Bundy to use before Ubaldo. Bundy could have gone multiple innings.
In any case, Ubaldo was supposedly on the roster as the long man in case Tillman went short. Well guess what? Tillman went short, and no Ubaldo. If you're not going to use him to start the 6th inning, I don't think you should use him until he's the last man in the bullpen.