Before a digital circuit can process a signal, it must first be quantized, an inherently analog process. Your digital data is only as good as your analog signal, plus inherent quantization noise[1]. In addition, any mixed-signal IC represents a design compromise between digital and analog constraints.
Any signal processing system is inherently limited by the SNR of its source signal. There is no point in building a more accurate converter than the noisiest component of your input data. In fact, when metrologists are trying achieve the maximum accuracy in their measurements, it is not uncommon to leave a test circuit on for days at a time, in order to reach a thermal equilibrium to minimize the seebeck effect[2].
And when engineers to need to make the most accurate of measurements, what do they turn to? Analog circuits. The world's most accurate voltage reference, the Kelvin-Varley Divider, dates back to the late 19th century[3]. For a modern example of a precision reference, see Jim William's excellent white paper, "Quantifying Silence"[4].
[1] http://en.wikipedia.org/wiki/Quantization_(signal_processing...
[2] http://www.keithley.com/knowledgecenter/knowledgecenter_pdf/...
[3] http://en.wikipedia.org/wiki/Kelvin%E2%80%93Varley_divider
[4] http://cds.linear.com/docs/en/application-note/an124f.pdf