Is X "a real word"?

This is the kind of "grammar" challenge that annoys me:

The epidemic of "importantly", with or without "most' or "more" has bothered me for some time. It has been well over 70 years since I studied grammar here in New York City, so forgive me if I err in terminology. Is "importantly" a real word; can something be termed as such?

What can possibly be going on the mind of someone who asks if a perfectly standard adverb (adjective + ly) is "a real word"?

(The person to whom the question was addressed, Michael Quinion, assumes the genuine objection here is to sentential "importantly" ("hopefully" is the usual object of this complaint) and defends the use of sentential adverbs (as he points out, even Garner accepts them). The "is it a real word" is dismissed with a sentence pointing out its age (1611).)