I fully agree. Zooming in on your example: I think by the definition of NVC on Wikipedia, "I need us to work as a team" is not a need as in "universal human need". It's the deposition of an assertion ("team work means not leaving work before all tickets are resolved"), wrongly or maliciously expressed as a need.
IMO the best way to respond to that would be "Aaron-santos, I understand that you feel disappointed now. Unfortunately I absolutely need to leave at X o'clock. How about we make a plan for tackling this insane workload such that everybody on the team feels supported?"
Precisely this. The book refers to the difference between a 'need' and a 'request', and what differentiates the two. In this case, this would fall under the category of a request, and is not considered NVC.
IMO the best way to respond to that would be "Aaron-santos, I understand that you feel disappointed now. Unfortunately I absolutely need to leave at X o'clock. How about we make a plan for tackling this insane workload such that everybody on the team feels supported?"