I don't mean to sound like someone either really intelligent or condescending, so please don't take this that way.
I think the problem is that some people aren't willing to accept that an infinitesimal is equal to zero. In calculus, differentials are used to "work around" places where zero simply can't be used, and the end result is a correct answer. So if we were to ask, "If x is equal to infinity, then what is (x-2)/(6+3x)?" we can't find the answer because we are dividing infinity by infinity. However, if we were to say, "As x approaches infinity, what value does (x-2)/(6+3x) approach?" then we discover that we can evaluate the answer, 1/3.
I think this applies here also. The person is trying to ask "Is 1.999 infinitely repeating equal to two?" and we can't really answer that question precisely, because it is hard to give infinity any meaning. But we can say that "As the number of repeating nines approaches infinity, 1.999... approaches 2." Correct me if I am wrong, but I think that is what mathematicians mean when they say that 1.999... is equal to two, just as mathematicians will define the the slope of a curve y(x), to be the infinitesimal change in y divided by the infinitesimal change in x, even when one could argue that a differentials are practically equal to zero. And yet, derivatives give real results.
So in conclusion, I think the whole discussion is not about conflicting beliefs about a mathematical truth, but simply about conflicting definitions.