I agree. In some parts of the country (like mine) high school football approaches a religious status, and digging on the field is a sacreligious act. Besides, the grass is so thick and interwoven that digging in it is like trying to dig through layers of burlap.
If a school has reason enough to hire security guards, you can bet they have reason enough to approach you and ask you to leave. Yes, you may be paying for that security through taxes, but that doesn't give you an automatic exepmtion from the rest of the population. If the police get involved they could charge you with destruction of public property, no matter how well you've filled in your holes.
I live in a part of the country where the kids don't have to go through metal detectors to get into class, and where common sense still reigns supreme. Around here the schools ARE treated as the public property they happen to be, with folks even bringing the kids to enjoy the playground equipment, throw a frisbee, let the dog run or watch the stars at night over the weekends. A guy swinging a detector doesn't even raise an eyebrow. The police have better things to do than get bent out of shape over it, if some crotchety neighbor complains it's the neighbor who's told to get a life and stop wasting the cops' time. But I won't hit a football field, I stick to the practice fields, playgrounds and common areas where nobody cares that I'm digging up a few coins.