There is zero evidence that anything changed in 2GR-FE internal components from 2012 to 2013 that would require it to use thinner oil weight. I have yet to see a different part number, its been analyzed before. All manufacturers moved to thinner weight oils to get CAFE credits. Read manual again, viscosity is recommended, and not required. Two different things.
A good example of Toyota back-porting and allowing thinner viscosity on vehicles that previously called for 5w-30

 

Jiffy lube told me the least I could put in was a semi synthetic. Any truth to this?

 

5w-30 in 2gr-fe, they added 0w-20 because of CAFE. Dont fall for it

 

ITS BS, you can put 5w-30 conventional if you want as per owner manual.
jiffy lube is a last place where you want to get an advice or take your car.