The misunderstanding is that you seem to be taking density in a very literal way, just dividing a number with a unit of area- while we're talking about it while taking other factors into consideration. According to the definition you just gave, a thousand people living in close proximity would be an urban area, which it... is not. It can even be just a single building. But, it would still not be urban, because that building's worth of people would not be able to support an urban infrastructure, administration, commerce, etc.

By any definition, 15k is just not a bustling metropolis, lol. That's not a diss, it's just that it's on the low end of the definition of a town.