"I need a new car."
Translation:Jeg behøver en ny bil.
I think that idea has come about for two reasons. Firstly, "å behøve" is considered the more formal of the two, and when dire needs are at play formality tends to go out the window. Secondly, it's a syllable longer; if you need something urgently you want to express that as succinctly as possible.
So yes, there's a tendency toward such a division, but no, there's no rule about it or anything in the dictionary to support it.