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Not an American. This (admittedly weird, illegal, and discriminatory) thinking reminds me the concept of Glass cliff: "The glass cliff is the phenomenon of women in leadership roles, such as executives in the corporate world and female political election candidates, being likelier than men to achieve leadership roles during periods of crisis or downturn, when the chance of failure is highest".
I agree with Brandin that we should not signal out panic attacks, or other mental issues. A person might suffer from acute migraine, hay fever, or cat allergy, for example, all of which can affect an "important client meeting or […] a production emergency". That said, it is a good idea to pick a job that will both be less affected by your condition, and doesn't have a negative effect on your health.
"we're really busy right now", "my time is limited this week", "critical deadlines this week" - Personally, I don't like these either. We are not always busy, or always have critical work: work time should be valuable anyway. We don't need a special reasons to avoid wasting time.