> It's not sensible for pushes to be implemented in a caching layer, because pushes are effectively the manual overrides to the User-Agent's own caching; conversely, the User-Agent's cache is perfectly appropriate as a cache, and doesn't need HTTP/2 Push to work.

By "caching layer" he probably meant a proxy or load balancer level cache not the user agent cache. It would make total sense for a load balancer to statistically discover relationships.