Is this a fallacy? It seems like an attempt to short-circuit Reason...

Quotes are generally a goldmine of fallacies simply based on the fact that they have to be short and are incomplete as far as being an argument, and often taken out of context. In this particular example, we don't exactly know what Branson's intent was, and this would give us some indication of fallaciousness on his part. For example,

"There is no way I would ask others go on Virgin Galactic flight if I didn't feel it was safe enough for myself, therefore you should go on a Virgin Galactic flight."

could be seen as a form of the Appeal to False Authority . If you, the reader, accepted this as a valid reason to go on the plane, you would be guilty of fallacious reasoning, as well.

Based on the quote and the situation, I would have to argue for Branson in that the quote was a more of a reflection of his confidence in his product than an plea for others to accept his authority blindly.