Here's my own answer:
OK, so I figured it out, largely thanks to this extended thread on macforums
However, I'm going to offer a summarized version here. Whoever's responsible for the ubuntu page on this (the one I linked to in my OP) really should get it changed. Those instructions just don't work.
Here's what you need:
Create flash drive files:
Start up UNetbootin. Choose the ubuntu iso as the source and the flash drive as the destination. When that's finished you'll get a warning that the USB is not bootable on a mac. That's expected.
Create partitions on hard disk:
Open Disk Utility and choose the internal or external disk that you're going to use. Create a 2GB partition on it, formatted to FAT32. Create another partition (you can choose FAT32 for this too) the same size as you want your final install to be (I have a 750GB internal disk on my mac, so I gave ubuntu 100GB of that).
Get device names:
Open Terminal.app on your mac and copy/paste this command (you can type it, but there'll be some more complex commands later that you might want to cut and paste to avoid errors)
From the output, identify both the flash drive and the 2gb partition. They will have names such as /dev/disk1s1 and dev/disk0s4 for example. Make sure you pick the right name, or you could end up doing some damage.
Open Disk Utility.app, and click on the flash drive in the sidepanel. Hit the 'dismount' button in the taskbar above. Do the same for the 2gb internal partition.
Move files from flash drive to HD partition:
Copy and paste this into Terminal, but DO NOT press 'return':
sudo dd if=/dev/disk1s1 of=/dev/rdisk0s4
Change the device names to match those you found in step 3. The first device name is source (the flash drive), the second one is the destination (the 2gb fat partition on your internal disk). Notice that I've added an 'r' before 'disk' on the output device. That's deliberate and you should make sure you add it too, as it speeds up the copy process considerably.
Double check that line is correct, then when you're ready, press 'return' and enter your admin password (it'll be invisible when you type it).
Remove flash drive:
When that eventually completes, dismount and remove the flash drive. You don't need it anymore.
Fix partition tables:
Restart your mac with the option key held down. From the rEFIt menu, choose 'sync partition tables'. Confirm with 'y' and exit. Then choose 'restart' from the rEFImenu.
Start up ubuntu live CD:
You should now see the Penguin logo. Click on it to start the Ubunutu Live CD.