Clean Install El Capitan in Macbook without any other Mac
The short answer is no. Without a different Mac you cannot download an El Capitan installer without first installing Yosemite on your Mac.

One way to do a clean install of El Capitan when only having one Mac and a Yosemite recovery partition is this:


Install Yosemite using the recovery partition. 
Go to the App Store and download El Capitan.
Use createinstallmedia to create a USB installation of El Capitan.
Then you can use that usb media to format and do a clean install of your Mac.


Optionally you could skip the usb installation steps all together and install El Capitan, let it upgrade the recovery partition for you and use the fresh recovery partition to format and reinstall El Capitan as a freshly installed OS.

Instructions on how to use createinstallmedia can be found here:
https://support.apple.com/en-us/HT201372

As a side note, have you tried if Internet recovery has a different version of the system compared to your local harddrive recovery. Hold Option-Command-R to start up from OS X Internet Recovery. As found here: 
https://support.apple.com/en-us/HT201314