Just another urban legend.
Your Tahoe was designed to run on 87 octane unleaded (85 octane at elevations above 3,500ft) towing or unloaded makes no difference.
If you use regular fuel and the engine runs well (which it will unless the fuel is bad or there is something wrong with the engine controls) then why spend the extra?

Years ago engines lacked the modern electronics they now have and would ping or detonate when placed under a load as the combustion chamber temperatures climbed, the engine in your Tahoe has a system that prevents this from happening.

An engine runs its best when it is right at the verge of knocking or pinging.
We have also discovered that the 5.3L engine gets reduced fuel economy when run on higher octane rated fuels.