Surprised me also, however I've never been a user of SMD mounted capacitors in my projects, so haven't been bitten by this. It appears the smaller the SMD package selected the more drastic cap Vs running voltage variations seen:
Note, first, that as the package size increases, the capacitance variation with applied DC voltage decreases, and substantially.
We see a steady improvement as we progress to larger capacitor sizes, until we reach the 1210 size. Going beyond that size yields no improvement.
As the capacitor vendors have made smaller and smaller components, they have had to compromise on the materials used. To get the needed volumetric efficiencies in the smaller sizes, they have had to accept worse voltage coefficients.
Remember too that the ceramic capacitor type designations, such as X7R X5R, and Y5V, imply nothing about voltage coefficients. Engineers must check the data to know, really know, how a specific capacitor will perform under voltage.
Finally, keep in mind that, as we continue to drive madly to smaller and smaller sizes, this is becoming more of an issue every day.
Lefty