I just installed 13.10 on my MBA 6,2 and I nuked my OS X partition in the process. This is what I did to install rEFInd without another operating system to fall back on, as long as one has the bootable live media still.
Install Ubuntu using the built in installer normally.
After you are done boot back into the live distro.
Connect to the internet and Download rEFInd and extract it.
Open a terminal (ctrl+option+T), change to the directory where you extracted the file. In my case I used 'cd Downloads/refind-the-version-I-downloaded'.
Type 'sudo ./install.sh --usedefault /dev/sdxy --alldrivers' where x is the hard drive and y is the partition you installed grub on. Since you are in the live distro, you can open Gparted and see which drive you're supposed to be booting from. In my case it was /dev/sda1, which should be pretty typical since the MBA only has the one hard drive, the partition will have boot in the flags area.
Type sudo Reboot, you are finished.
REFInd will show up and you will be able to boot normally.
...profit?
Other people's mileage will vary I assume, but I am typing this right now on the machine I did this to: 13" Macbook Air mid 2013, 4th generation core i7 (yes, you can get an i7), 8 GB (7.7GiB) ram. Hope this helps you or any of the 50 some odd people that viewed the post at the time of this writting. Take care!