A physics-informed reduced-order model for the response and peaks of the vertical bending moment of a ship in irregular waves was introduced recently in the naval architecture literature, explaining the asymmetry seen in the probability distribution function of the moment and showing potential for its statistical extrapolation. The model involved a number of approximations: the disregard of heave, the use of Taylor series expansion, pitch averaging, the (improved) Grim effective wave, and the focus on the Froude-Krylov and hydrostatic component of the moment. These approximations are reexamined and justified here from the time-domain perspective by arguing first that the distribution of the moment in irregular waves is captured by that on regular waves with random amplitudes, and then assessing the effects of the approximations for the ship on those random regular waves. It is also shown that the peaks of the reduced-order model can be computed semi-analytically when random regular waves are used for the excitation.