You can't boot the 10.8 installer if the 10.9 recovery partition is present. You have to delete the partitions (using the 10.9 boot disk or other tools) first.
This is not correct. I have booted 10.8 installers just fine on a few computers running Mavericks with a recovery partition. I reckon the culprit is the USB installer. I am going to assume you have a Time Machine backup of 10.8 for the first set of instructions.
--Time Machine restore:
-Boot from your Time Machine drive by selecting "Option" at startup.
-In OS X utilities, erase and re-format your boot drive to a 1 partition HFS+ Journaled drive.
-Run "Reinstall OS X" from the OS X utilities window and choose restore from backup, selecting your latest 10.8 backup and you're done.
-- USB drive clean install (no Time Machine)
-Make sure you are properly creating a 10.8 USB boot drive. Follow these instructions:
http://arstechnica.com/apple/2012/07/how-to-create-a-bootable-backup-mountain-lion-install-disk/
- Boot from USB drive by selecting it in System Preferences or by selecting "Option" at startup.
-In OS X utilities, erase your 10.9 boot drive and re-install 10.8
I can't stress enough the importance of a good backup, especially if you intend to downgrade. Time Machine is fantastic and combined with Migration Assistant, they make a powerful combo to manage multiple OS X versions, backups, data transfers, clean installs, etc.
Good luck!