That seems really strange to me - just not a lot of serious side effects to worry about with Diamox when the alternative is AMS in a dangerous setting. And 14K' is most definitely AMS territory, regardless of the crystal ball the doc was peering into to be unconcerned about altitude affecting you.
Any chance he might have misunderstood and thought you were asking for dexamethasone? Dex is a powerful steroid used at elevation when AMS symptoms present themselves. Diamox, typically used prophylactically before an ascent, just isn't a big deal for most people. I ask because, with my wife's prior history with debilitating AMS, she discussed dex with her doc last year - just to have a tab available up high if AMS nailed her again. Even with her history he adamantly refused to prescribe it, based exactly on what you relate your doc said - serious side effects outweighing the benefits. He does, however, prescribe Diamox like candy.