why do americans (wrongly) consider statistics a field of mathematics?

[angus]

It isn't "wrong."  The world isn't so black and white, Walter.  Just as biochemistry, physical chemistry, and nanotechnology are degree options within undergraduate chemistry departments, statistics and actuarial sciences are degree options within undergraduate mathematics departments.  This is not always the case, of course.  Several schools such as Villanova and Swarthmore actually have a "Department of Mathematics and Statistics" (possibly in an effort to squelch a fissure.)  In other fields this has become common as well.  There are departments of biochemistry and departments of physical chemistry, and when I have spoken to department chairs about this they usually claim that renaming departments "Chemistry and Biochemistry" and the like relieves some pressure.

If you think it's wrong, then you should look at the much larger picture and conclude that it's all wrong.  The main reason to separate the disciplines the way we do is due to history and tradition.  For example, when national labs take out ads for combustion researchers, they often announce that they're looking for a PhD in physical chemistry or chemical physics.  They don't really care which, so long as the candidate is an expert in the specific field of interest.  I also remember in graduate school two italians students who had undergraduate degrees in physics, and who were certain that what they were studying would be in the department of physics in Italian universities.  On the other hand, I was always comfortable characterizing thermodynamics, kinetics, statistical mechanics, and quantum mechanics as chemistry courses, or as part of the general chemistry curriculum.  At conferences in my field, I am equally comfortable talking shop with physical chemists and physical chemists. 
 
There are probably many different ways to organize academic disciplines.  Putting statistics experts in mathematics departments isn't the worst organizational scheme I can think of.  Statistics and combinatorics overlap well with discrete mathematics and even graph theory.  In the United States, statistics is generally approached from a standpoint of probability theory.  At least the undergraduate statistics course I took was taught like that.  There may be other ways of approaching the problem of housing statistics.  You are certainly free to use your funds to endow the creation of a university in which statistics will be a stand-alone department with its own faculty and its own pedagogy.  Accrediting agencies can be somewhat conservative, though.  Okay, I'm being a bit snarky, but the larger idea that we might occasionally re-think curriculum isn't always a bad one, especially if the goal is to prepare students for economic opportunities.

[angus]

You are certainly free to use your funds to endow the creation of a university in which statistics will be a stand-alone department with its own faculty and its own pedagogy.  Accrediting agencies can be somewhat conservative, though. 

http://www.stat.ncsu.edu/

Yes, walter, as I indicated I am aware that some have separated.  I am also aware of Departments of Biochemistry (which broke away from chemistry) and Departments of Genetics (which broke away from biology, which is particularly ironic since Biology and Genetics were considered different branches of science about a hundred years ago anyway.) 

The fact that North Carolina board of regents allowed this does not, however, mean that they "wrongly" consider statistics not a field of mathematics.  Such schisms happen from time to time in universities, and they are complex, and usually have political underpinnings, and sometimes personal ones.