There are a couple of bits of truth here, sort of...
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The very-low voltage capacitors (say, 10V and less) are generally trying to squeeze the maximum capacitance into the minimum space, and may be sacrificing close tolerances to do so. It wasn't uncommon for Aluminum electrolytic capacitors in general to have tolerances of -10/+80%, for example, which was OK because in the typical applications it was "more uF is better."
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The latest generation of exotic ceramic dielectrics (X5R, Y5V?), which permit things like 100uF 6V caps in an 0805 footprint (!) apparently have "quirks" that affect the tolerance (things like capacitance being unusually dependent on applied voltage, for example.)
So while it's not true that voltage rating has a direct effect on accuracy, it MAY be true that a capacitor whose voltage rating is particularly close to the actual applied voltage has a less accurate value than a more conservatively specified capacitor...
Read your data sheets! If you can find them (some of the linked DS's at digikey didn't have much more than physical measurements 
)