One can keep the door shut, yes. It is kind of a weird system. The plug is actually "held in" by the plug stops in the frame (12 of them). The plug stops align with 12 mating stop-mating-pins and contact (on the plug, e.g. "door"). The way the plug gets into that position is "interesting". It tilts up from the bottom on the two lower hinges. Then it is lifted "up" so that each plug contact point and pin rises "above" the corresponding door stop. Then the door is pushed "in", so that those same contact points are now in a plane "hehind" the door frame stops. Then the door is lowered down, so the pins align with the stops. Normally air pressure would keep the door's pins and contacts aligned with the stops. But on the ground, when there is no pressure, the door needs to be secured from "upward movement". Its really, backward movement (push-in to release the pins from the stops, AND THEN upward movement, so that the pins and contacts then clear the door frame stops. Then in a control removal, the door is pulled out from the top, the pins and contact clearing the frame contacts, and hanging in the air on the hinges, and some straps. Then the door is supported, the straps removed, and the door lowered, or totally removed.
The job of the 4 bolts is to "hold" the already placed and aligned pins/contacts that are in contact with the door frame stop brackets, in the "outward direct contact position. These bolts also serve to prevent the door from translating "upswards as well." The pins also prevent upward alignment, but they are not as strong, they are really for alignment. The contact point bracket (with a pin in the center), and the door frame stop bracket really hold the door against air pressure.
The bolts keep the door from pushing back into the plane (on the ground, with no air pressure), and also present the door from "sliding up" such that the door contacts and the frame contacts would not longer contact.
The alignment and door plug placement (for insertion, and removal) is aided by guide tracks on the panel, and guide track rollers that are mounted to the door frame.
On flight 1282, the door plug's roller tracks were described as badly damaged.
Any one of the door plug "retention" bolts properly torqued would have been adequate to hold the contacts with pins, in position. Any two (one top, one bottom), properly torqued would have been adequate to prevent roller track damage from vibration, door weight, in flight turbulence induced vibration. All four provide dual redundancy. (Two diagonals, or two, one up, one down.) While the NTSB has been totally silent thus far, it seems that the bolts were likely missing in their entirety, or all 4 bolts were so loose, that the bolts backed out until missing, or only one or two "lose" bolts remained. The bolts don't work if there are not tightened to torque spec for holding the door plug contacts in place against the door frame stops.
So, yes, this assembly did in fact have typical critical system redundancy. And it hard warnings on the pressurization system on whole (many possible causes). While Boeing or supplier (or probably BOTH), and the FAA all failed in new plane inspection, AlaskaAir failed with the pressurization warnings. (3 prior faults.) Extremely disappointing how the entire manufacturing chain, and operational chain BOTH failed here for this event to occur.
Really, cannot call this event an accident. An accident is something like the torque wrench being mis-calibrated. (Though that is still a manufacturing or maintenance fail.) But in this case, supplier fail, Boeing fail, FAA fail, AlaskaAir (3 times fail). Pretty despicable really.