If an analog of Aumann's agreement theorem applied, then the bids would always add to 13. Why do they differ (let's say, to be more specific, that the bids are less than 13; the logic applies similarly to being more than 13, with the obvious modifications)?
One condition that may explain it is that players not be bidding perfectly: overall, players are underestimating the strength of their hands. Another reason is that players are not perfectly confident that other players are bidding perfectly: Bob may see Alice submitting a low bid, but not be sure whether that low bid is due to a bad hand, or due to the Alice underestimating the strength of her hand. So Bob will not adjust his bid as much as he would if he were sure that Alice's bid was due to her having a bad hand. Players also could lack confidence that other players are confident in other players' skill. Suppose Alice and then Bob both submit low bid, and Charlie is next to bid. If he were certain that Alice and Bob are perfect bidders, and that Bob knows that Alice is a perfect bidder, then he would conclude that Bob must have a very bad hand, to bid low even after learning that Alice thinks she has a low hand. But Charlie might think that Bob thinks that Alice might have underestimated the strength of her hand. If Charlie thinks that, then his estimation of Bob's hand's strength will be higher than if he were certain that Bob is certain that Alice is a perfect bidder. It's not necessary for Bob to be uncertain of Alice's skill, only that Charlie is uncertain whether Bob is uncertain of Alice's skill. And of course, if Debra bids next, and she is uncertain as to whether Charlie is uncertain of whether Bob is certain that Alice is a perfect bidder, that can cause Debra to underbid. Thus, a low total bid can occur if the players have hands that look individually bad (but aren't as bad as they look, because the other hands are also bad), and the players don't have perfect meta-knowledge.
The other way that Aumann's theorem fails to hold is that the bids are not iterative: Alice has no opportunity to adjust her bid upon learning that the other players think that their hands are bad. Any decent player, if they did have such an opportunity, would tend to adjust their bid upwards. The earlier the player bids, the less information they have from the other players' bid, and so the more likely their bids are the source of the total underbid.
Another factor is that the cost of overbidding, versus the cost of underbidding, are not generally the same, and players will err towards the direction with a lower cost. So a total underbid could mean that players are uncertain how many tricks they can take, and underbidding is less costly than overbidding.
So, overall, a low total bid suggests that the later players actually have bad hands, while the earlier players have hands that look bad individually, but aren't actually as bad as those players thought they were, because they were unable to take into account how bad the later players' hand are. However, low skill or low metaknowledge regarding the other players' skill can complicate this analysis, as can nonsymmetric cost functions.