There are two ways to download Mavericks on pre-installed systems.
1. Restart using Command+R to boot into the Recovery HD. From the OS X Utilities Menu, select Reinstall OS X.
2. Restart using Command+Option+R to boot into Internet Recovery which boots into Apple's servers and their Recovery HD. From the OS X Utilities Menu, select Reinstall OS X.
The above 2 methods will download AND install Mavericks to the target drive.
What you might try is the following to extract the necessary file(s) to create a USB thumb drive installer:
- Plug in a formated USB external drive (not a USB thumb drive unless its 32GB) and point to that drive to install to.
- You will have to watch the download and when your Mac restarts after the download and at the black screen, unplug your external drive. You should boot to your normal Desktop.
- Plug your USB external drive back in and look for an InstallESD.dmg file. It might be in a folder named something like "OS X Install Files". Copy it some where like your ~/Downloads folder or your ~/Desktop.
- Download DiskMaker X 3.0.3. When prompted for the Install OS X Mavericks.app file, point to the InstallESD.dmg file from the above step. Point to a USB thumb drive (8GB) as the destination drive.
I don't know if the above steps will work as I don't have a Mac with Mavericks pre-installed. But I got that last step from the DiskMaker X FAQ under the question of "I got my version of OS X pre-installed with my Mac. How can I get the OS X installer ?"