Graduate training programs from other departments, how helpful are they?
Yes, as @JeffE attests, there is at least a balance to be struck in the diversification of your skills and perspectives versus having a clear focus that will mark out your niche. You can overdo either one. My perspective, as someone who has been involved in inter-disciplinary research for 15 years, and who has had a lot of advice from much more senior folk about this, does err somewhat on the side of Carroll. In particular, your goal is to mark out a well defined territory that is not too diffuse. "Trajectory" in your career (mainly your pub record) is a primary consideration for hiring and promotion, and it's difficult to build up a body of work if you dabble in many areas.

My own perspective resonates with Carroll's here: continual, long-term dabbling is Bad for getting tenure. It will dilute what others will be able to confidently perceive/predict about your current and future impact in a specific field. But being a "drone" who just followed faithfully in the footsteps of his/her PhD mentor, using the same perspective that might already be "old-fashioned" and not future-proof to the growing inter-disciplinary pressures (you should be able to insert your own field-specific examples here!), is also Bad. Either because you find eventually yourself bored or devalued as a "mere follower" rather than innovator, or because your micro-focused view dries up in terms of peer interest or funding.

Remember that institutions at least pay lip service to inter-disciplinary work. Some actually really support it in a meaningful way, and look for fresh, innovative thinkers to join them. As a junior academic, now is a good time to explore what's not too far from your area and learn more about how to position yourself with a unique and/or highly desirable set of skills and body of knowledge. So, this can be exactly how you end up being successful in contributing in a clear direction in exactly the way I interpret from Carroll's blog post. 

For you, ask your mentors and colleagues how they see the current and future combination of the two disciplines you are talking about, and what the interesting questions are. Then try to see how you could fit into that and do something innovative while remaining feasible and concrete. It's tricky, but finding that sweet spot should get you a long way, and it could be much more rewarding. Just be careful who you work for. Some places or people talk the talk but don't walk the walk. When it comes to decisions involving money, if your institution's administration or your peers don't know how to properly evaluate your highly innovative inter-disciplinary work then you might "fall between the cracks" and be passed over for a more traditional candidate whose work they can, at least, easily understand! Good luck