"On the grounds" probably has the "reasonable person" definition and thus would not likely include a public sidewalk. Where it could get murky is when sidewalks go through a campus grounds of a school that is K - 12. I can't think of any examples, but there may be some.
The more I read the interpretation from the Senior Counsel of the Office of the Wisconsin Legislative Counsel to Senator Pam Galloway the more I am struck at just how modest the training requirement is. Any NRA Course that included instruction in firearms safety will do, any military training that included firearms will do, any hunter safety course offered in any state will do.
And in a twist that few states do, WI equalized out of state permits for the 1000 foot GFSZ (translation: free kill zone). It would still be a federal offense, but one would have to have the State involve the Feds. (UT considers any out of state permit to be equal to a UT permit for purposes of the UT GFSZ.)