Not a good comparison, at all.
People are sitting literally inches away from each other in a stadium and they are vertically stacked where the person behind them is maybe 6 inches away.
The most accurate way to take a measurement is to do it by grid. A high quality aerial photo of a 100’x100’ area, take a head count and extrapolate to the entire area used with a +/- used to deal with the less populated areas of the sample.
It seems odd that someone has not done exactly as you say with the clean aerial and grid count. You are of course correct.