Smoothing doesn't affect your data points, it's just an alternative method of connecting the dots. Hence, the issue of whether they're representing the "original data" doesn't really apply. Smoothing only affects how the interpolation makes the discrete data points into a continuous trend. For example, if your data has points for x = 1 and x = 2, smoothing would give a "not necessarily" guess as to what the value at x=1.5 would be, as would linear approximating.
It sounds like the issue your skeptic has is whether you can accurately infer what that value is, and the answer is "no", but you can take an educated guess. You can forecast, spline, trend, regress, etc. But, at the end of the day, the Intermediate Value Theorem doesn't apply to discrete functions.
I'd explain it that way, or switch your graph to an X-Y scatter plot with just discrete points if your skeptic has about as much of a chance of understanding what cubic beziers are as my boss would.
