I agree with you; that is exactly what I thought when she said that. Having worked for the federal government for many years myself, I learned fairly quickly I needed to 'fuzz up' my job description for people outside of my specialized area/agency, especially if they did not work for the government. I translated my job description into a very general, somewhat vague title that is easily understandable to most everyone (but greatly over-simplifies what I actually do).
Now having said that, I do agree Meredith (or CMT if they made the call) did not choose the best general term as "diplomat" does carry a more formal/high-ranking impression with the general public, as rightfully noted in this discussion. I wouldn't have even tried to put a specific title on their jobs; I think it would've been better if she'd said something like 'we work for the State Department, supporting diplomatic activities at the American Embassy' for example. Maybe it would be too 'fuzzy' for CMT (who may have wanted to deliberately inflate how important their jobs sound), but it also might've been more accurate and not raised so many questions. And frankly, although still deliberately vague, saying something like that still makes their jobs sound pretty interesting to me..!