The cargivers were bullying and needed corrective action.
The behaviors of the cargiver crossed the line when they neglected their duties and impacted patient care. They did this willfully and with complete disregard to the patient's wellbeing.
Based on the story as stated by OP, she did not commit any acts of workplace aggression against the staff. In fact, I would not even say she disrespected them. Contrary interpretation is completely baseless.
Professionals are to respect others personality traits. Being social in the way YOU prefer is not mandatory of any team member. You are to do your job, and maintain respect objectively.
"Not saying hi" is not being disrespectful. Nor is not making small talk. That is such a stretch. How do you reconcile this with cultural competence? In fact, to JUDGE someone because they do not communicate with you the way you like is disrespectful. Not the other way around. Disrespectful act they also committed include the acts of gossip and sarcastic remarks.
You are required to show up and do your job, and be respectful. You are not required to engage in small talk, gossip, banter be any ones friend for that matter. You are to be a colleague. If someone were to "require" all this of me... Sorry. It is not something I do, and you have to accept that, just as I accept your extroversion. Just because you have decided to be upset doesn't automatically mean I have committed an offense against you.
Work place tension is not enjoying someone but not committing offenses. When it became gossip, sarcasm, and isolating- it was then bullying. But when it involved patient care, it crossed a line that no nurse should excuse. It absolutely needed corrective action.