As the map you voice recordings to an id and map that id to your apple id, I find it very strange they can claim it's anonymous!
Muller pointed out, however, that the identifiers are deleted immediately—"along with any associated data"—when a user turns Siri off on his or her device. (You can do this by going to Settings > General > Siri on a supported iOS device.)
If you can delete the identifiers and associated data when disabling Siri, it is not anonymous.
Also voice recognition has been working fine for many years now, if they want to find your voice clips it shouldn't be much trouble.