While its possible that its a downstream effect of CBR 1/2 we can't jump to that conclusion, the pharmacology of CBD is absurdly complex and biochemical inflammation pathways may be tangential to IRE1α which is part of the ER stress response
>Mounting evidence suggests that there are novel cannabinoid receptors[10] that is, non-CB1 and non-CB2, which are expressed in endothelial cells and in the CNS. In 2007, the binding of several cannabinoids to the G protein-coupled receptor GPR55 in the brain was described.[11]
>The existence of additional cannabinoid receptors has long been suspected, due to the actions of compounds such as abnormal cannabidiol that produce cannabinoid-like effects on blood pressure and inflammation, yet do not activate either CB1 or CB2.[25][26]
https://en.m.wikipedia.org/wiki/Cannabinoid_receptor
>Cannabidiol may be an antagonist of GPR55, a G protein-coupled receptor and putative cannabinoid receptor that is expressed in the caudate nucleus and putamen in the brain.[70][71] It also may act as an inverse agonist of GPR3, GPR6, and GPR12.[72] CBD has been shown to act as a serotonin 5-HT1A receptor partial agonist.[73] At higher concentrations, CBD acts as an inverse agonist of 5-HT1A receptors.[74] It is an allosteric modulator of the μ- and δ-opioid receptors as well.[75] The pharmacological effects of CBD may involve PPARγ agonism, inhibition of voltage-gated cation channels, and intracellular calcium release.[14]
https://en.m.wikipedia.org/wiki/Cannabidiol
On a discussion of ~65 possible protein targets for CBD:
>Some CBD effects at these targets in in vitro assays only manifest at high concentrations, which may be difficult to achieve in vivo, particularly given CBD’s relatively poor bioavailability.
https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC4604182/?r...
Here's an alternative receptor for your inflammation theory: A2
https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC2588644/?r...