Jeremy: Check out the book The Unthinkable: Who Survives When Disaster Strikes, And Why, by Amanda Ripley. There are quite a few works about the psychology of disaster now available, but this is by far the most accessible.
Your question can be answered from several different perspectives.
A) If you are told "There is no danger, this is a formality" and you see virtually NO sign of danger, why WOULD you choose to be among the first?
B) "Cover your ass" comes into play big time, particularly in cases where large numbers of passengers are lost. I've used this comparison before, and doubtlessly will again, but when the liner San Juan sank during the summer of 1929 IN LESS THAN TWO MINUTES, in the dead of night and with everyone asleep, the passengers had a better survival rate than those aboard the Titanic; a slowly sinking ship whose lifeboats left pathetically underfilled.
A common factor among shipwreck accounts, if you take the time to study ONLY first person accounts collected in the first week or so after the disaster, is the split between "The passengers would not cooperate" and "The crew failed miserably." The thing is, the passenger accounts tend to reenforce one another, while the crew accounts don't. That is to say, if a passegner witnessed something and wrote about it while the memories were still fresh, chances are good that you will find an identical account BY SOMEONE ELSE who witnessed it. ANd, these are people who did not know one another, did not communicate with one another, and were writing accounts not intended for public reading.
With the Lusitania, for instance, you have over two dozen accounts in which people who did not know one another described a "fat" crewman who came down the port boart deck and ordered the already loaded boats offloaded. Mr. Myers identified him as his bath steward. You have two dozen or more accounts of people who then stood by their lifeboats, growing progressively more angry, until in the last few minutes a couple of boats were "officially" reloaded and lowered, and several others were filled by passengers who climbed in hoping that they would break free as the ship sank. All details match.
Now, with the crew who were on the port side, what one finds are tales of panicking women, hysterical foreigners, and gallant struggles to push boats "uphill" against the list as time ran out. Thing is, they don't reenforce one another and they dont mesh, at all, with what the passengers saw.
This pattern repeats with the Vestris; the Morro Castle; the Andrea Doria, and The Yarmouth Castle. Invariably, in the split between "The passengers behaved illogically and then panicked" and "The crew failed miserably," the passengers fare better than the crew does in terms of mutually supported stories.