I think that zero number comes from a Richman and Earnest paper called Electoral Studies. It didn't say that there were zero illegal votes, they said the percentage of illegal votes was zero meaning that that there was such a small amount of them when rounded to the nearest number it would be zero.
The numbers shown in this article however make it relevant. Usually the first argument I get from someone about illegals voting - or even plain old voter fraud - is *first*, it doesn't happen (which is ridiculous and easily disproved) and when you SHOW that it is not true, the response THEN is, it's insignificant. This is to bolster the argument they hold that requiring ID to vote amounts to suppression of votes - an argument that NEVER makes sense because elderly, poor, minorities all require SOME simple form of ID just to do ordinary things.
The reason why I do NOT believe it is insignificant is, fraudulent voting - or illegals voting - is not spread evenly over the entire nation's geography. It is concentrated in areas, because illegals are concentrated in areas. We have had two presidential elections where the electoral count could have moved the other way on a VERY small number of voters. It DOES matter.
And I've said often, that as much as people pule and whine about voters being disenfranchised, a vote cast illegally disenfranchises all of us.