Compiling the list just for fun.

Starting with WWII era, "shot at" limited to military
situations

FDR No
Truman Sorta yes, but I will say No
Ike No ( strange but true )
JFK Yes ( but mostly rammed )
LBJ Yes ( but pretty much bogus )
Nixon No
Ford Yes ( in an impersonal way )
Carter No
Reagan No
GHW Bush Yes
Clinton No
GW Bush No

Analysis:
Overall; 4 yes, 8 no

Dems 2 yes, 4 no
Repubs 2 yes, 4 no

Presided over a significant war as president 3 yes 4 no

Didn't
1 yes 4 no

Service academy graduates 0 yes 2 no

Army/AF vets 0 yes 4 no
Navy 4 yes 2 no

Conclusions: Damfino

Maybe there isn't a real pattern.

Bob McKellar