I had to use those monitors my freshman year of high school. The only thing the teachers used it for was to make sure we kept our heart rate over a certain amount of beats per minute for however long we were supposed to be exercising. Basically, the whole point was to make it harder for us to slack off while the teacher wasn't looking.
What they didn't count on was that I figured out how to set the minimum heart rate to whatever I wanted, effectively letting me get an A by strolling leisurely around the track. As far as I know, I'm the only one who figured out how to do it, which isn't saying much for the rest of the class since it took less than 5 minutes of experimenting with the menus for me to figure out how to do it.
Don't worry about your privacy on this one; I don't know of too many PE teachers who give enough of a shit to compile a database on all the kids and their data. Also, the monitors are shared between classes, so it would take quite a bit of work to figure out whose results were whose.