Members of the NFHS Officials Association receive insurance for ALL levels of sports recognized by the state high school association. This covers youth as well as adult sports and is not restricted to high school games.
So, since MSHSL recognizes fastpitch softball, I am covered by the NFHS insurance if I officiate women's fastpitch (for example), but not men's (since MSHSL does not recognize boys fastpitch).
NFHS Officials Association insurance covers general liability and excess accident medical. For accident medical, you are first covered by your own insurance (e.g. through your day-job employer), and the NFHS insurance picks up where that leaves off. Insurance is provided by Dissinger Reed.
National Federation of State High School Associations - Dissinger Reed
I've never had to file a claim, so my knowledge is based purely on what I have read, not what I have experienced.
However, it does mean that when I register with USA, I am double paying for insurance I don't need, and unless I was going to officiate sports not recognized by the MSHSL, I certainly would not benefit from NASO insurance.