Obviously we're both playing "what ifs." We don't know what would have happened in seventh (mine), we don't what might happen today or tomorrow (yours), and we don't know the relationship between player and manager.
It's worth noting, though not mentioned above, that Rocco took the unusual step of visiting the mound with two outs and two runners on base in the sixth AND LEFT HIM IN. As Chief notes above, it would have been a perfectly logical time to take him out. I'd suggest that leaving him in at that point is exactly his manager letting him get out of the jam.
But in situations like that, the conversation is rarely, "If you get this guy out, I'll let you pitch another inning." It's usually, "I've got confidence in you. Put all your focus on this guy, and we'll call it a day."
I'd also say that the damage to his and the team's confidence and the gut punch it provides if he pitches poorly in the seventh is way more substantial than the gain that comes with him going one more successful seventh inning.
And lost in there is that up 3-0 in the seventh was a perfect time to get Fulmer back on the horse after a loss on Wednesday night.