99% correct. They are also under the CiC when they are active - either if they are deployed, or under their 2 week training each year. Normally though they are only under federal control if they are deployed to a war or a military action for something like a humanitarian effort. You are correct that the governors are their CiC unless they are federally active.

There is one interesting thing as well that I noticed with Operation Lone Star in Texas. Some states loaned guard troops (along with some that just sent law enforcement) to Texas, and they would be under the TX gov while they were on temporary duty. I mentioned that because I could see some states sending guard troops to NY to help with dealing with the illegals, like they did for Texas.

Incidentally, many guard families use the 2 week training period to visit military medical facilities while they are active and can partake. The rest of the time they either use some other insurance, or they can buy a special insurance available to the guard and reserves.