There is a simple solution to this:
Drop all of the _dta_... statistics and stop blindly applying DTA recommendations.
More information
The particular problem was that there were multiple sets of statistics for the column in question. The extra dta statistics were created by sampling the data (the default behaviour for statistics not associated with an index).
As is often the case with sampled statistics, the resulting histograms did not cover the full range of the unerlying data. The query in the question happened to choose a value that was outside the histogram, resulting in a 1-row estimate.
The exact behaviour of the query optimizer when multiple sets of statistics exist for the same column is not fully documented. It does tend to prefer 'full scan' statistics over sampled, but it also prefers more recently-updated statistics to older ones.
