Earlier quoted context omitted.
Neither intel nor AMD supports core boot. Community efforts to add core boot focus entirely on intel because of market share (although intel is also plenty hostile to floss in this regard).
Not sure about the support. Intel employees regularly submit to coreboot repo. I know at least for the Atom based designs that I've been involved in Intel provides reference designs using coreboot and supports it.
They support it to the extent it is required to support due to contractual obligations for chromebooks or other vendors who may have similar deals with Intel. I doubt if Intel actually sees coreboot as something worthwhile outside of a shim to load FSP. To that end, they have also create a BSD licensed project called slimboot (more like shimboot) which exemplifies that approach better.