Very recently, diffuse gamma-rays with 0.1 PeV < E _γ < 1 PeV have been discovered from the Galactic disk by the Tibet air shower array and muon detector array (Tibet AS+MD array). While the measured sub-PeV flux may be compatible with the hadronic origin in the conventional Galactic cosmic-ray propagation model, we find that it is in possible tension with the nondetection of Galactic neutrino emissions by the IceCube neutrino telescope. We further find that the presence of an extra cosmic-ray component of relatively hard spectrum, which is probably related to the Cygnus Cocoon region and other PeV cosmic-ray sources in the Galactic disk, would alleviate the tension. This scenario implies the existence of an extreme accelerator of either protons or electrons beyond PeV in the Cygnus region, and predicts the continuation of the gamma-ray spectrum of Cygnus Cocoon up to 1 PeV with a possible hardening beyond ∼30–100 TeV.