But I don't think the conclusion follows, and it certainly doesn't seem to be rational behavior on the part of the participants. While fear may drive their decision, the mentality that would lead the participants to focus all their efforts on preventing the worst possible outcomes regardless of cost or likelihood is the mentality of an irrational fear.
A more rational perspective is to consider not only how poor off the worst are, but the chance of being born into that lowest station. If the demographics of society are such that 10% are poor, 10% are rich, and 80% are middle-class, then a rational agent would not structure society to benefit the poorest of the poor. Instead, they would discount the measures to benefit the poor by the chance of being poor (among other considerations such as the relative values of different stations). The same reasoning would apply even more strongly to considerations such as being able-bodied, since almost every person is. This would essentially lead to a form of probabalistic utilitarianism. Now, humans tend to naturally be a bit more pessimistic than a purely rational agent would be, but we see those who are maximally pessimistic (e.g. those with acute phobias) as having problems with their ability to reason.
Also, different people would have different levels of risk-aversion. Even if we found the level of risk-aversion that would be most satisfactory overall, it would almost certainly not be the maximally pessimistic one. Therefore, the original position would almost certainly not lead to equitable starting points in society. I'm not trying to make a value judgment about whether this is desirable. I'm only arguing that the veil of ignorance is insufficient to make everyone want such a society. If, to get around this, you denied them information about their society's demographics, they could use average demographics. If you denied them that, it would seem to merely deprive them of the ability to make decisions informed by how the world actually is, and I don't see how it would lead to an optimal policy. Clearly the idea of the veil of ignorance is important, but I don't see that it has resolved the long-standing tension between people's desire to serve their self-interests and their desire for fairness. At the very least, merely being ignorant of one's station is not enough, and a more specific kind of ignorance needs to be found.