If I buy a full retail Windows 8 license am I granted the right to install a down-level version of Windows, specifically Windows 7, instead? Just to be clear: I buy a full retail Windows 8 license - full version (not upgrade) and retail, not OEM. But rather than installing Windows 8, I want to run Windows 7. Is this allowed?
No. Downgrade rights (which is what I assume you're thinking of) only applied to the Vista/XP era.
If you want to buy a license for Windows 7, there is nothing stopping you from purchasing an OEM license, or buying it outright from an online retailer.
Unless you buy an OEM license of Windows 8, which more information is available here.