Well, just over three years later, the New York Times attempts to answer just that question, in the article Can Burt’s Bees Turn Clorox Green?
If you don't want to read the three page article, we can cut to the chase:
To prove his own bona fides, Mr. Replogle grabs a bottle of Burt’s Bees avocado butter hair treatment, squeezes some onto his finger and dramatically licks it off. He then passes the tube to two Clorox executives so they can have a taste.
“If you can’t put it into your mouth, you shouldn’t put it on your skin,” he says. “I’d like to see other companies do that.”
Funny, because I have a little sample tube of the avocado butter hair treatment that I want to taste... I mean... err... try.