That is correct. "Disturbing the Peace" also has a specific legal definition involving fighting, threatening behavior, excessively loud noise, etc. in a public place. Playing loud music in your car that rattles the windows of homes in the neighborhood is an example. Ganging up on a peaceful protester in a threatening manner is an example. Allowing your dog(s) to bark for prolonged periods is an example. using offensive language with the intent to incite violence is an example. Knocking on hotel doors in the middle of the night would even be an example. Actions that "jeopardizes others right to peace and tranquility" is generally a qualifying factor. There is no "peace and tranquility" at a political rally. There is no evidence that the protesters were doing any of those things. If anything, they were guilty of "being annoying" which is not a crime.
There is a big difference between peacefullyarching and holding signs and activly trying to disrupt an event by shouting the speaker down to interfere with his right to free speech and the audience right to listen. It'*s the same as if you brought noisemakong equipment to rock concert to try and drown out the sound. You would rightfully e arrested for disturbing the peace.
I know that when i protest, it's always someplace other than where the people I'm protesting are located. I have found that's the best way to draw attention to the cause or person I'm protesting.