Humor, Truth, and Accurate Language

When someone says something followed by "just kidding," I take notice: truth, or at least that person's perception of the truth, is wrapped up in the joke.  Whether this is a good delivery method for delicate news or not, I am not sure (what do you think?).
Here's a humorous link that points out a perceived language error:  the inaccurate use of the word literally.

https://www.youtube.com/watch?v=9jh4Mpgbi4A

What do you think of the humorous critique? Is there truth in it?  What is the issue, if any, with using an otherwise harmless word incorrectly?