well its a forum so things will get questioned, life's to short to spend it worrying that you might need a video of people and do a search on here about photographers getting falsely accused of spying on kids.
I just think it opens up more issues than it might solve, but each to there own.
I would get a cheap version of a go pro. Would work well, as body harness is available for these, if you search on the equipment section there is a thread on them.
out of interest what would you of done with the footage if you had it after being mistaken for someone else, and would you have it on running all the time for the one or two times you need it?