so are you are saying is that it never makes any sense to use the word coercion in a general sense out side of relevant event context? Are you saying it never makes any sense to say he is being coerced but rather this should always be qualified by saying either he believes he is being coerced or i believe he is being coerced? if this is your meaning than i agree. It seems that what is in question is how one should interpret the meaning of the statement "he is being coerced", whether it should be interpreted as meaning he believes he is being coerced or whether it should be interpreted as meaning i believe he is being coerced.
Belief doesn't enter into it. You can objectively determine who is using coercion in any conflict where coercion is being used by determining who initiated the conflict. The other party, who did not initiate the conflict, is defending themselves.
I don't like to claim that we can be objective. We can agree to enough aspects of word definitions to make the subjectivity insignificant (that's what we do in math), but true objectivity is ... well, void, in my view. But that's probably a bit too philosophical a discussion to have here.
To answer the question of how we should interpret one person's claim that some guy is being coerced, trust, but verify: I would ask the victim: "Do you feel a threat to violate your rights?" Whether or not the victim holds my definition of coercion, an honest answer will provide me with the understanding I desire. From there, I can judge those doing the threatening and interact or avoid them, defend or abandon the victim, and explain whatever choices I make according to my voluntaryist disposition. I might have to ask what the threatened rights are first. But that's the rub - if I agree that the victim has those rights, then I agree that it's coercion. If not, I and the victim will have to agree to disagree - not because of the facts of the situation, but because we don't agree on what rights the victim holds - about whether he's being coerced.
"Threaten" and "harm" and "damage" and "violate" are simpler than "coerce" because "coerce" requires a certain psychological state in the victim - essentially his belief that he would be better off without the person doing the threatening. To use "coerce" as I use it requires that you believe something about the victim's beliefs. I suppose I'm narrowing the definition from how most people use it - people who wouldn't be puzzled by "He coerces the horse" because "threaten" and "coerce" mean the same thing to them. I think that requiring the victim to perceive that he has some rights that are under attack makes "coerce" more useful - and I think when people use it - honest people, not politicians - there is at least a tincture of that requirement.
I brought up the horse because I've been using the difference between horse whispering and horse breaking for years to explain what's wrong with government authority and everything it touches, and also in discussions about raising children.