I had a similar situation in this afternoon's games. Up one run, top of ninth, THREE relievers available (rested, ready to go), "Use Mop only when Losing" checked, and Sparky brought in the Mop. He allowed an inherited runner to score on a FC (interesting line: 2/3 IP, 0 H, 0 R, 0 ER, 0 BB, Blown Save) and I won it in the bttom of the 9th, but still ...
And as for not using a mop-up, I ususally don't for the reasons cited herein. Sometimes, though, a Theme's limits almost force you to go with one.