> factual statement
Those are measurements, prone to their own biases and variances.
> make a factual statement
People make statements for reasons. "Just stating facts" still, usually, says something other than the fact being stated, and that other thing is usually the actual goal of the message.
> stereotypes vs statistical differences
It's not quite an either-or scenario. The act of stating something was, by itself, neither a stereotype nor a statistical difference. The measurements being stated were not stereotypes. The reason you stated them might have been because of or in service of a stereotype, and derived statements (like "asians are good at math") might be stereotypes.
> negative stereotype
This is a bit harder to pin down to a definition. Stereotypes are "negative" when they're untruthful, misleading, unhelpful to the stereotypers, disproportionately damaging to the stereotyped relative to the stereotyper's gains, .... If you apply some combination of "for God's sake, don't be dicks to each other" and "despite best efforts, people think I'm a dick, maybe I should reflect on that for a minute" then you'll probably do all right for yourself.
Picking on incarceration rate as an example (I know you were asking about the nature of negative stereotypes, but let's assume you brought it up in some other context, just to have a hypothetical to work with), what purpose is stating that measurement serving? It doesn't help you with any decision you might be able to make, including parole, avoiding shadowy alley figures, hiring, lending, (even when legal), .... It strongly suggests something interesting going on, but there are too many obviously confounding variables to have a snowball's chance in Hell of using that statistic to make an informed decision about almost anything. Bringing it up, except in the context of using it as evidence that we need more data for something, is likely to happen because of and in service of a negative racial stereotype, and in most contexts that's how I'd interpret anyone making that statement.