This doesn’t sound like anything dangerous.

A few black specks, or even a small dark piece, in otherwise normal stool is just undigested food. The details you gave actually point away from bleeding:
it was a small amount
the rest of your stool looked normal
it broke apart easily and kind of crumbled

When stool is black from bleeding (melena), it’s:
uniformly black, not spots
tarry, sticky, and smeary, not dry or crumbly

What you described, especially that straight edged piece, lines up with something like vegetable skin.

As for the ER part, doctors there are trained to think worst case until it’s ruled out. If someone says there’s black in my stool, their first instinct is to check for blood. That doesn’t mean they think it is blood, they just don’t want to potentially miss anything. I used to work in the ER, and it was the same approach

In non emergency or online settings, it’s more about patterns. You describe what’s going on, and we compare it to what’s textbook.

So the difference is: the ER leans toward testing to be safe, while outside of that, we can usually sort things out based on how it actually presents.