CO2 hydrogenation: should hydrogen be the headline?

A lot of CO2-to-methanol and CO2-to-fuel writing starts with the catalyst. I am not sure that is where the public claim should start. The hydrogen source usually decides the carbon result before the reactor does.

Useful anchors: Porosoff et al. on catalytic reduction routes (doi:10.1039/c5ee02657a), Jiang et al. on methanol hydrogenation (doi:10.1021/acs.chemrev.9b00723), and Ye et al. for a recent wider view (doi:10.1126/science.adn9388).

How would you phrase a fair claim for thermochemical CO2 conversion if the H2 is only "planned renewable" rather than measured renewable?