I have found the accuracy of a CMM is more related to the workpiece, set-up and operator, than it is to any inherent machine error.
Assuming that the machine is in good condition and was calibrated correctly, yes ±0.0003 inches is a reasonable expectation BEFORE all other inaccuracies are considered.
If you are shooting a small metal part with a short, low-force touch probe and a rigid set-up, you could achieve that (or better) on a DCC machine.
On the other hand, if you have a large plastic part with a long probe with a manual machine and a trainee CMM operator, expect ±0.005 inches (if you have a good tailwind :).
We have DCC, Manual, and video CMM's and both expert and trainee operators and shoot all kinds of parts (we are a contract CMM lab). Our most accurate machine has a B89 ball bar of 0.00050 inches, BUT it seldom achieves that level of accuracy. On some parts it will, but on most, it is higher.
The trick is to gain experience with different parts and set-ups.

An important rule when inspecting something for the first time on a new set-up is:
ALWAYS DOUBLE-CHECK DEVIATIONS - you should be able to change your set-up and get the same numbers, or use a height gauge or pins, etc. to back up your deviant readings.
A CMM is not a magic wand, it does not always produce correct results. It is a very versatile tool that, because of it's versatility, can easily get bad numbers on good parts unless watched carefully.