Here's my opinion on this. If you think a little about the question, the intuitive answer is this: while confidence interval describes the range of mean values for a sample, accuracy of a statistics describes margin of error in measuring values. This relation is not to be confused with related, but different, one of accuracy and precision: http://en.wikipedia.org/wiki/Accuracy_and_precision. Actually, I believe that these relations represent exactly the same things, with the only essential difference being reversed terminology - what your question and much statistical materials refer to as confidence interval and accuracy, the above-mentioned Wikipedia article (and potentially other materials out there) refers to as accuracy and precision (see Figure below).

A detailed and IMHO very good explanation of a relation of and difference between confidence interval and accuracy can be found in the Chapter 20 of the second edition of Julian Simon's book "Resampling: The new statistics": http://www.resample.com/content/text/24-Chap-20.pdf. All chapters are available online here: http://www.resample.com/intro-text-online.
More confusing (to me), but nevertheless good and more statistically-focused explanation is this: http://www.bioconsulting.com/calculation_of_the_confidence_interval.htm.
Finally, another relevant discussion can be found here on Cross Validated site: Narrow confidence interval -- higher accuracy?.
It should be noted that often some papers, including statistical ones, use the term "accuracy" to denote a different meaning in a specific context, for example, to describe the ratio of true results of a medical diagnostic test to all results: http://www.lexjansen.com/nesug/nesug10/hl/hl07.pdf.