That's a good point, but on the other hand, even thinking that everything is a Gaussian would be a vast improvement over thinking that everything is a Dirac delta and it is therefore not ludicrous to speculate about why some politician's approval rating went down from 42.8% last week to 42.3% today when both figures come from surveys with a sample size of 1600.
A well trained mathematician or physicist who never took a formal course on statistics likely isn't going to make that error, just as a well trained statistician isn't going to make that error.
I would think that the mathematician is more likely to get this right than the medical doctor who got statistics lessons at med school.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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