When is it incorrect to draw stacked area charts? Stacked area charts work great when charting raw values, averages, counts, and percentage of total. The sum of the values across the different groups will add up to that of the entire set.
But what about in the case when the value being charted is a Median, Geo Mean, or any Percentile? In these cases the sum of the values (say Media) across the categories will not add up to the Median value of the entire set.
Example: We have the data on the consumption of Meat, Vegetables, Fruits, and Dairy for a country. For each category (and the entire set) we have the median pounds consumed per person, each year, for the last 10 years. If we were to draw them in a stacked area chart, the sum of the values for a given year would not equal the median pounds consumed per person across all the categories.
Is it fair to assume that the stacked charts should be avoided in these cases as they will cause confusion?
 A: You already answered your own question: you shouldn't use a stacked area plot for any statistic for which the the statistic of the total is not the unweighted sum of the statistics over the component categories. In other words, the statisitic must be a linear operator. The arithmetic average, count, and total are all linear operators, but the median, geometric mean, and most other statistics aren't.
However, in your example case, I doubt that the difference would be massively noticable just from visual inspection from a plot. Have you tried plotting it to see what happens? You could plot the stacked area chart of the median, then plot a line with the true median over the top.
BTW, does this dataset exist? It would be quite a useful teaching tool, and would make a great addition to R's dataset package.
A: The simplest rule is that it is incorrect to use a stacked area chart on any day of the week ending in a 'y' (may need modification if used outside of English speaking locales).
If you are interested in the total, then plot the total and don't include the chartjunk formed by the other groups.
In a stacked area chart you may be able to interpret the total and you may be able to interpret the line that is on the bottom, but it is very difficult to interpret the other lines, you need to judge the difference between the line and the one below it which is much harder than than just looking at individual lines.  If you are interested in the individual lines then plot them against a common scale, not distorted by stacking.  If you don't care about the individual lines then they are distorting and distracting chartjunk.
