Monsieur hAAmer, not all flights are suppost to start boarding at 35prior to departure time. Some at -30, some at -20, depending on the equipment. (sorry, at home right now so I don't have the grid)
I can tell you that after doing HUNDREDS of flights, a few have gone late. When I fill out late reports, I can honestly say I have NEVER put the blame on the passengers. In fact, I don't know any agent who has. Do you?
PS if you still are coming to the gate at -35, thank you.