Good question Ryan. The article doesn't say what land lizard snakes are closely related to, but snakes may have branched so far back that it (the ancestor) might already be extinct and further may not be present in the fossil record. However, any other lizard "lines" that are derived from the same ancestor would share a few traits (base pairs?) with snakes. Any genetic testing with those species would point to a common ancestor.
"We can exclude monitors - that's statistically supported,
I guess this means genetically monitors and snakes don't share a lot. That's pretty darn shocking.