Is it a bad idea to say in my statement of purpose that I want to pursue a PhD in applied mathematics primarily to work in industry? I am seeking some general advice from applied mathematicians at American universities. In my statement of purpose, would my stating that I want to pursue a PhD in applied mathematics primarily for the purpose of working in industry be a bad idea, in general?  

This would be sort of "keeping it real" and being honest, when knowing that the vast majority of phds will end up in industry and not in academia, where jobs are extremely scarce.

Or is it still better to tell them what they want to hear?  I am assuming that what they want to hear is that I want to be an academic and make contributions to teaching and publish in academic journals, etc.
I have done graduate admissions for my math department.  I am a "pure mathematician" but my department is just the math department: there is no formal separation between pure and applied.

Others can speak for themselves, but I always find honesty refreshing, and the idea that a prospective PhD student does not want to pursue an academic career does not horrify me: rather, in some ways it relieves me.  Moreover, if you know this "all along" and don't disclose it right at the outset, when will you disclose it?  There is no natural time until you are graduating / going on the job market, and then it will be way too late for your programmatic experiences to be tailored to your true goals.  

The worry here, I suppose, is that you risk looking "less serious" than other applicants.  In my opinion you can completely counteract this by including, a plausible, specific post-PhD career plan in which having a PhD plays a natural role.  That is, don't say "I don't plan on pursuing an academic career" or even "I plan on pursuing an industrial career", say which industrial career you are aiming for and why the PhD will be helpful and/or necessary.  Math PhD programs would like to have students with specific, realistic future plans that they can work towards steadily during their time in the program.  We don't see many such students, but we would like to have them anyway.