The API endpoint for Docker is actually just the ProGet server root, as that is what the Docker client requires. Feed names in this case just act like an image prefix.
Because of this limitation, the only way to verify requests were intended for Docker was to check the UserAgent string, as /v2/... is a pretty generic URL, so that's what ProGet did.
This was never a good solution, so we've removed this check for v4.7.11, which should allow other non-Docker clients to use the Docker API more easily (see PG-1023). If we're ever in a position where something else expects the /v2/ URL prefix, we'll reevaluate this solution again.