I'm not sure about the 56367 being the state of the art. The $30,000 Mark Levinson No. 40 is arguably a state-of-the-art product and they use the SHARC processor from Analog Devices.
I don't believe DD/DTS are bit-exact decompression algorithms. Therefore one processor that decodes a DD/DTS bitstream may produce a different set of digital samples than some other processor. That would imply that different decoders will have a different sound. However, all DD/DTS decoders have to be certified by Dolby/DTS, insuring some level of quality, before being allowed to claim compatibility or use the logos.
Also, any post processing that goes on (beyond decoding), such as bass management for example, would certainly alter the sound. And as Sean pointed out, the supporting electrical circuitry will also have an audible effect. Power supply, clocking, DACs etc.