Cross-origin could be an HTTP server itself serving content from a different origin via a push channel (which it could do either because the different origins share servers -- which can occur -- or by having, e.g., prefetched the data itself from the foreign server and pushing it.)
HTTP/2, I'm pretty sure, doesn't allow this (and there are all kinds of reasons it wouldn't be a good idea), but it wouldn't necessarily require forcing the other server to push the content.
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Cross-origin could be an HTTP server itself serving content from a different origin via a push channel (which it could do either because the different origins share servers -- which can occur -- or by having, e.g., prefetched the data itself from the foreign server and pushing it.)
HTTP/2, I'm pretty sure, doesn't allow this (and there are all kinds of reasons it wouldn't be a good idea), but it wouldn't necessarily require forcing the other server to push the content.