You could also look at it from the perspective of set theory. "Injuries" is a set of n members, {I} = [I1...In], and if you interpret "None" to be equivalent to "Zero", zero being defined as an even integer, "None of the injuries are" sounds right.
Here's another example: "None of the band is on stage" vs. "None of the band are on stage". This one is interesting because there's cultural context too. The British tend to look at things like "the band" as a plurality (i.e. a set) and would say "are", whereas many Americans look at "the band" as a single entity unto itself (that happens to be composed of multiple people) and would say "is".
Shall we also bring up "the United States are" vs. "the United States is"? Same concept, and it's a telling question to ask because the USA as plurality was the norm for most of our history. The more modern USA as singularity says much about political development (and mostly for the worse).