Competent data miners will have some statistical background, yes, but many interesting data mining technologies have come out of other fields, such as computer science. There are many types of data mining (predictive modeling, clustering, text mining, association analysis, etc.). The important thing is to understand the particular real-world problem, identify which (if any) data mining techniques can be applied, and to use them appropriately.
The field is a promising one, depending on one's skills and location. I imagine that right now, a competent data miner couldn't throw his or her resume up in the air in Washington D.C. and have it hit the ground due to recent interest in the intelligence community (FBI, NSA, CIA).