While I've dabbled with various instruments and styles over the years, over the past 6 or so years I've zeroed in on almost exclusively playing one style on one instrument, so I'm inclined to agree with Diller. But I'm curious to see what other perspectives people have.
From http://www.dwightdiller.com/faq.html
A student should pick the instrument that s/he feels COMPELLED to play and work on that to the exclusion of the others. ... It's hard enough trying to learn the instrument that is burning in your heart to play without wasting time on another instrument only to go to what you really want to play.
I continue to see students picking up a second instrument when they hardly have a clue how to play the first instrument. Yes, there are a handful of people in this world who can very quickly become proficient on any instrument, but they are probably not to be trusted if they are that good. HAHA. I remember the WVa fiddler, Wilson Douglas, saying to a person, whom he had helped on the fiddle, but had just arrived with a spanking new banjo, looking for affirmation: "Why don't you go give that thing to someone you hate?" Wilson had grown up in the tradition and understood what kind of sacrifice it takes to learn the music. How can someone who has not grown up in the tradition have any possibility of learning two instruments well? ... I am speaking from experience: choose your instrument carefully and then invest all of you, all of yourself in it. ... Forget shortcuts completely. This, then, will give you the greatest payback for your investment over the years. That doesn't mean that you can't plunk or saw around on the another instrument farther along, but it does point out that you won't become a master of two instruments on a given kind of music. No matter what kind of music. And reality is, you better stick with ONLY ONE kind of music; you cannot do it all. ... Question: which burns in your heart to play? which one do you feel compelled to play? Go with your heart, your spirit. It won't lie.