They are very picky about documents, which is a good thing considering how high their fines are... A common problem at DFW, for example, is that US passengers to Brazil will get a Brazilian visa, but don't realize that you have to enter Brazil within 30 days of the visa's issuance. Even if it is a 5-year visa, it becomes invalid if not used in 30 days... I've never seen a Brazilian customs guard look at the dates, but the AA agents always do.

In other words, not having a passport is an even bigger deal.