Jesse has a good point - here in MA all it takes is the perception of a threat to cause a world of hurt. Very few cops will bet their careers on accepting the LTC holder's claim the complaintant is lying or mistaken. Police have their own version of of "killem all and let god sort em out" - "just make the arrest and let the court figure out who is telling the truth".
Some people are so afraid of guns, they can actually imagine they are threatened if they see a holstered handgun. This can result in a "perception" of a threat, going so far as to imagine steps went beyond what actually happened (accidental display becomes an intentional threat and attempt to intimidate, hand on the gun becomes drawing the weapon, etc.). The most credible form of inaccurate eye witness testimony is that which is honestly believed to be the truth by the person telling the tale (as countless cases of persons convicted by compelling eyewitness testimony, only to be later exonerated by DNA analysis demonstrates). So, the gun owner not only has the risk of someone willing to file a false report, but the risk that they will be on the wrong end of an unfortunate failure to communicate.
Shoot someone's dog that is worrying you or your livestock? No problem - covered by MGL. Dog owner perceives, or alleges, that you threatened them with a gun while shooting their dog - plea bargain or felony trial.
If the other party doesn't know you are armed, the chances of that person alleging you threatened him/her with a firearm are greatly reduced
To follow up on Rob's point, probable cause is such a low standard of proof that if the responding officers determine the "victim's" statements are credible, then cuffed and stuffed you go. Scary stuff.