Exile is only for the criminally negligent. For example, if someone is swinging an axe and the axe-head flies off and kill someone, the person must flee to an ir miqlat (city of refuge). But if the axe head comes off because it struck the wood being chopped, or a chunk of the wood flies off and kills the person, he doesn't need to flee. It has to be the person's direct action, not indirect. Similarly, if someone falls off a ladder and kills another, he only is sentenced to exile if (1) he is descending and (2) the ladder was known to be rickety. (These cases are on Makkos 7b-8a.) It is only for deaths where we could argue that someone who took like more seriously could have prevented the tragedy.
Given that the person must carry a measure of culpability, a literal read of this verse doesn't seem tenable.
Perhaps the verse is a source for the Kuzari's idea in 5:20 (slightly de-thou-ed from Hartwig Hirschfeld's 1887 -- and therefore public domain -- translation; formatting with bullets, mine, but the text mentions "three other categories" so I know the intent was to list 4 items):
... My opinion is that everything of which we are conscious is referred to the Prime Cause in two ways, either as an immediate expression of the divine will, or through intermediaries. An instance of the first kind is found in the synthetic arrangement visible in animals, plants and spheres, objects which no intelligent observer would trace back to accident, but to a creative and wise will, which gives everything its place and portion. An instance of the second kind ... is to be found in the burning of a beam.
You may even discover the causes of their causes till you arrive at the spheres, then at their causes, and finally at the Prime Cause. One might justly say that everything is ordained by God, and another is equally right in making man's free will or accident responsible for it, without, however, bringing it outside the divine providence. If you like, you may render the matter more intelligible by means of the following classification. Effects are either of divine or of natural origin, either accidental or arbitrary.
The divine ones issue forth actively, having no other causes except
The natural ones are derived from intermediate,
preparatory causes which bring them to the desired end, as long as no
obstacle arises from one of the other three classes.
ones are likewise the result of intermediary causes, but accidentally,
not by nature or arrangement, or by will power. They are not prepared
to be brought to completion and standstill, and they stand apart from
the other three classes. As regards the arbitrary actions, they have
their roots in the free will of man [see below -mb], when he is in a position to
Free will belongs to the class of intermediary causes,
and possesses causes which reduce it, chainlike, to the Prime Cause.
This course is not compulsory, because the whole thing is potential,
and the mind wavers between an opinion and its opposite, being
permitted to turn where it chooses. The result is praise or blame for
the choice, which is not the case in the other classes. An accidental or natural cause cannot be blamed, although some of them admit a possibility. But one cannot blame a child or a sleeping person for harm done. The opposite was possible just the same, and they cannot be blamed, because they lack judgment.
Notice Rabbi Yehudah haLevi here has his protagonist classify free will choices as being indirectly from G-d, as are arbitrary actions. Which would fit ascribing murder by criminal negligence -- somewhere in that spectrum between choice and arbitrary -- to Him.