Yes Russ. You are pretty much right.
Fever is a defense mechanism, but fever is a risk too if it is too high and causes damage to the person as well as to the disease.
So while fever is a symptom up to a point after that point it becomes a complication that has to be dealt with in its own right.

Temperatures above 106 degrees Fahrenheit can result in brain damage and possibly death. That high of a fever is pretty unusual and a very high fever is indeed an emergency situation that needs to be reduced.
Ice packs and cold baths might even be needed.

Up to about 102 or 103 degrees you are likely better to just make sure they have plenty of fluids and let them sweat it out, but above that you need to start worrying about the effect of the fever itself.

I don't know if the blood thinning effect would matter.