Understood! My point was that, while dimensional analysis almost always works (including for this problem), you have to make sure you are using the right dimensionful quantities. In this case that there are constraints here due to orbital mechanics that were not respected, and hence the 12,000km is way off.
To successfully apply DA in this problem, we should start by noting that since we are talking about impact, it is a foregone conclusion that the earth and the asteroid will be in the same place at the same time (your application instead was related to figuring out where earth and asteroid would be in relation to each over at a given time).
Once you've specified that they will be at the same place, asking where it lands _on earth_ amounts to asking which part of the earth will be facing the asteroid at that time. Since there is a quoted uncertainty of +- 10min, the range of outcomes is almost entirely defined by the angular distance that the earth with travel in those 20min -- about half a time zone!
This gets us much closer to the actual projection from ESA. The actual central location at the nominal time is defined almost entirely by the direction the asteroid is approaching from -- i.e. the relative inclination and phase anomaly of the orbits. So, the rest of the projected range can be chalked up to uncertainty on the geometric fit of the object's orbit based on astrometric observations. Which we can't apply DA to without further information.