I'm late to this party, but I'd point to the fact that many of the states Cruz lost in the south have open primaries:

https://en.wikipedia.org/wiki/Open_primaries_in_the_United_S...

Actually, the following states were lost by Cruz and have open primaries:

Alabama, Arkansas, Georgia, Illinois, Indiana, Mississippi, Missouri, North Carolina (All races' primaries open for unaffiliated voters only), South Carolina