To me, the word accident implies something that happens without apparent cause and/or there was nothing that could have been done to avoid it.
That’s cherry picking a small part of the common definition of accident.
Accident, noun:
1) an unfortunate incident that happens
unexpectedly and
unintentionally, typically resulting in damage or injury.
2)
an event that happens by chance or that is without apparent or
deliberate cause.
Your definition is only the part I made yellow, but as you can see there is a lot left out if you just look at the yellow text.
Negligence has both a common and a legal definition.
Common: failure to take proper care in doing something.
Legal: failure to use reasonable care, resulting in damage or injury to another.
In the common definition we see the word “proper” which is a subjective judgment. You can refer to anything, including intentionally shooting a chosen target, as negligent if your personal idea of “proper care” is strict enough. For example someone could believe that shooting edible objects as targets for fun is not proper care of food and so everyone who shoots melons and pop bottles is by that standard negligent. They aren’t wrong, they just have different values.
Many of the stories posted here meet the common definition of negligence, as long as “proper care” is defined as following all four rules at all times. That doesn’t mean they aren’t accidents as well.
As for the legal definition of negligence, a few of the stories posted here meet that definition, but it isn’t the majority.
Whenever you have ambiguous words that can have different meanings, and “negligent” with its combination of a common subjective definition and a legal definition that has a specific meaning certainly qualifies as ambiguous when used in an online forum post, there is wisdom in thinking carefully before using that word. There are alternatives such as “unintentional” or “accidental” that are less prone to being twisted to an unintended meaning.