Newer BLRs are chambered for the various Winchester short magnums that are operating in the 65000 psi range. Given that info, I can see no reason why they couldn't handle the Hornady Light Magnum cartridges. Especially since the Hornady catalog states that they have obtained the velocity increases without any additional pressure. For a comparison, the SAMMI specs for the 308 Winchester recommend maximum pressures of 62,000 psi.
The issue with autoloaders the Hornady refers to may have something to do, in part, with the gas operating systems they utilize. I personally wouldn't hesitate to try it in a BLR - I have shot handloads in my BLRs that were producing obvious pressure signs without incident - BLR actions are pretty strong.
You can also contact Hornady and try to get a more specific explanation:
http://www.hornady.com/contact_us.php