I would disagree. I say that everyone should take a first aid class, but to be useful in any real situation in general you need a shitton of training. Honestly, from experience, I want fewer people who think they are useful when being everything but useful in emergency situations. It leads to situations where I need to babysit them and work. At worst, they endanger themselves and/or others.
I know a lot of people who are not used to these situations feel like an extra pair of hands is always a plus but I have not met any first responders, health care workers, military or aid workers that agree with that statement. It is a common subject of discussion as it really is driving most of us up the wall.