Chris,
Your explanation is correct. The neutral position for the hammer is slightly off the firing pins. For that reason, a half cock and hammer safeties were not needed.
When the hammer fell, the momentum carried it past its neutral position to strike the firing pins. The hammer spring would bring the hammer back to its neutral position.
Now some rifles were made with rebounding hammers and half cocks; An Austrian double rifle I had was made with both rebounding hammers and half cocks.