Looking at the results for Doug Burgum, compared to results in the 2012 and 2014 Primary, it does not look like Democrats had as much of a role as they would like to think or that the NDGOP insiders would like to think. Doug Burgum got 410 fewer votes against Wayne Stenehjem than Rick Berg got against Duane Sand in 2012.
In 2012, the general belief was that Democrats wanted Sand to win because he was the easier target than Berg. Also in 2012, Brian Kalk was the Republican Convention-endorsed candidate and he got 1,615 more votes against Kevin Cramer than Wayne Stenehjem had against Burgum. Then if you look at a low turn-out year in 2014, you see that when there was no primary contest, Kevin Cramer got 50,188 votes and George Sinner got 30,102 votes - in a low turnout year. Compare that to Marvin Nelson's vote count of 17,126 and you can see where the hard-core Democrats are vs. the casual Democrats.
Even if you assume that an equal number of Democrats crossed over as voted for Marvin Nelson, 17,000 fewer votes for Burgum still would not flip the race back to Stenehjem. So no, I do not think there is a statistically provable case that Democrats crossing over were solely at fault for the Stenehjem loss. (See graphic above for source numbers.)