It sounds like the OP's doctor is overracting.
The rationale to withhold NSAIDs in patients with UC has been suspect for some time. It was believed that NSAIDs would cause a flare. However, when the methodology of the study was scrutinized, it was found to be flawed.
It was thus: Of patients who ended up in the hospital with a UC flare, how many had taken NSAIDs in the past two weeks (30 days?). From there it was determined that NSAIDs will provoke a flare.
However, people pop these things like candy. As an analogy: Of patients who ended up in the hospital with a broken leg, how many had taken NSAIDs in the past two weeks? No one would suggest causation in that case. . . .
That said, and what probably provoke the study, NSAIDs are hard on the GI tract (and liver and kidneys).
I've taken NSAIDs with UC all along, and I've never had a problem. I'd use my own good judgement and experience in guiding my choices.