I am a little torn between realistic business demand of paying least money to get jobs done and thorough mastery and understanding of theories. Look at biostatistics; there master graduates become data analysts and process data. They know the nomenclature and can understand instructions from more advanced statisticians. The majority of practitioners don't know proofs and they carry off their tasks reasonably well. I would call all but very select few statisticians applied statitisticans and the world is fine with that. I am not sure machine learning industry will not turn out like this, although I am not looking forward to that day.
I would just note that numerical optimization is a big deal in machine learning while I know of no statistical department strong in it. The popularity of SVM owes a load of gratitude to pracitical breakthrough in dynamic optimization. But if one elevates to the level of functional approximation then statistics is similar to almost all engineering fields. In fact, I suspect statisticians have more common with engineers than scientists. I bet Eric Cantor didn't care that polling results had margins of errors but that he lost his House seat due in part to overconfidence coming from unreliable statistics. Real world applicability, not theoretical nicety.