Why can't I format my blank SSD from OSX Recovery?
Use Disk Utility from a working machine

I don't know why this didn't work in recovery mode, but a friend suggested I plug the SSD into a working Mac with a USB adapter and try using the working Mac's Disk Utility to format the drive.

I did, and that worked. Now I'm installing OS X on it using recovery mode.

Maybe (I'm speculating) the version of Disk Utility that I have recovery mode (my computer came with Mountain Lion) doesn't know how to work with SSDs?

In any case, Disk Utility on a machine running El Capitan was able to format the drive via my USB adapter.