I believe your statistics may be wrong. I tried a google search and the results were inconclusive, but I think one article said 14% of accidents were by those with no insurance and of those 14%, 80% were by illegal aliens (which comes to about 10% of the total) The 80% figure came from cheathouse.com and is anti immigrant and of a dubious source.
However, the numbers of 14% by uninsured and 10% by illegals (or 80% of uninsured) fit my intuition.
I will add that since illegals have trouble getting valid driver's licenses, they will also have trouble getting insurance since they can't get a license, so the 80% sounds right to me. Plus 1 of 7 being uninsured sounds right to me also.