Also, there is a world of difference between professions where accidents are common, and a profession where humans may be actively trying to kill you.
A hero might be a person who knowingly risks life and limb for the safety and wellbeing of others. Even more heroic when those others are strangers (ie it is more heroic to rescue a stranger's child from a house fire than it is to rescue your own child from a house fire). Even more heroic than that is when you do it day in and day out(ie it is more heroic to be a firefigher, saving strangers every day, than it is to save a stranger once).
So, if that is a reasonable analysis of heroism, some police can definitely be heroic. I'm not sure about the percentages though. I'm sure some police got into the profession because they wanted to be a big man with a gun. Others did it because they want to help the community they live in.