I am not an expert on AIAG, but I assume that 'the process' means that you would compare the measurement error to the acttual variation of the process (study variation or historically observed variation). if you know that the Ppk value is greater than 1 then you know the process variation is less than the tolerance and the measurement study turns from focusing on the measurement system's ability to distinguish between 'in-tolerance' and 'out-of-tolerance' parts to the system's ability to detect changes (such as with SPC)...
If any AIAG experts out there can correct my interpretation or add insight it would be appreciated!