This week’s fact-checking video from CNN’s Jake Tapper and FactCheck.org shows why Kansas Secretary of State Kris Kobach does not have “proof” of widespread voter fraud in New Hampshire that could have helped Democrats win a close U.S. Senate election.

Kobach, who is also the vice chairman of the Presidential Commission on Election Integrity, wrote in a Sept. 7 op-ed for Breitbart that “now there’s proof” that “out-of-staters take advantage of New Hampshire’s same-day registration and head to the Granite State to cast fraudulent votes.” His so-called proof is that more than 5,300 people who registered to vote on Election Day with an out-of-state driver’s license have not since registered a car or gotten a driver’s license in New Hampshire.

But that isn’t evidence of any illegal voting. There could be several explanations for that.

In a joint letter sent to New Hampshire House Speaker Shawn Jasper on Sept. 6, New Hampshire’s Secretary of State Bill Gardner and Commissioner of Safety John Barthelmes wrote: “It is likely that some unknown number of these individuals moved out of New Hampshire, it is possible that a few may have never driven in New Hampshire or have ceased driving, however, it is expected that an unknown number of the remainder continue to live and drive in New Hampshire. If they have established their residence in New Hampshire, they may have failed to obtain a New Hampshire driver’s license.”

It is also plausible, even likely, that most of those voters were college students who are allowed by state law to vote in New Hampshire even though they only live in the state part of the year and maintain an out-of-state driver’s license. An analysis in February by New Hampshire Public Radio found that “the towns that see the highest rates of out-of-state IDs used at the polls are all home to college campuses.”

“Probably most of them [those who registered using an out-of-state license as ID] are college students, but it’s hard to tell how many,” Fergus Cullen, a former chair of the New Hampshire Republican Party in 2007-2008, told us in a phone interview.

“What Kobach and the commission are conflating is a state law they don’t like with massive fraud, and they are two different things,” Cullen said.

Watch the fact-checking video here and read our article, “Kobach’s Bogus ‘Proof’ of Voter Fraud,” for the complete analysis. All of our past collaborations with CNN’s “State of the Union” are available on our website.