I think that training is important. I think you need to learn as much as you can learn. I would say that it's important and probably crucial, but I wouldn't say that everyone has to have it.
The word liberal distinguishes whatever nourishes the mind and spirit from the training which is merely practical or professional or from the trivialities which are no training at all.
I fear - as far as I can tell - that most undergraduate degrees in computer science these days are basically Java vocational training. I've heard complaints from even mighty Stanford University with its illustrious faculty that basically the undergraduate computer science program is little more than Java certification.
I certainly love a boogie and once the music starts I'm usually one of the first out there on the dance floor. Although I haven't had any formal dance training and something tells me I'm really going to notice the difference.