Regarding vocabulary, I think when Celia (apparently a government or at least airport employee) uses the word "dispatcher" she is referring to whomever at the company is filing the flight plan. That person essentially discarded her observations, told her to calm down, said "this is the way we do it, we've done it before, I'll take care of it, it will be shorter than 4:22, so shut up."
What her legal authority was is unclear, but she ultimately gave in to the badgering of someone who for some reason she perceived as having superior authority.