If you had an Avery swatch book, you could have lifted up the strips and looked at the back to see for yourself. Not all of them are white on the back. Perhaps your color would have been able to been "close enough" with another manufacturer's color.
The Avery cast vinyls are really thin, almost translucent. The white is there to keep the color even on a dark surface. My logo's PMS color is 375, which Avery happens to carry. I do not like using Avery, but since they have "My Color" I've had no choice. I've wrapped nearly all the equipment in our shop, and had spray paint custom matched for things that couldn't be wrapped. I have wrapped Red and Blue welders (from you know who brands) with my Green, and you can't even tell there may have been another color underneath. It's because of the whiteout backside to the vinyl. Yeah, it sucks on things where I would have like to have a reverse mount, but there's always paint and/or double sided mounting adhesive.