Okay, let's think this through with a particular case.
Assume only your two factors: John has a reliable source of income and overdraft protection on an account. Since you assert that those two factors are sufficient, we can suppose John doesn't have any line of credit, doesn't own anything valuable that could be converted to cash, doesn't know anybody that could give him a loan or a job, etc
John donates all his savings, and loses his job the next day. He has overdraft protection on his empty bank account, which will save him from some fees when he starts bouncing checks, but the overdraft protection will expire pretty quickly once checks start bouncing.
Things will spiral out of control quickly unless John is able to get another source of income sufficient to cover his recurring expenses or there is some other compensating factor than the two you mentioned (which shows they are not sufficient). Or do you think he's doing okay a month later when the overdraft protection is no longer in effect, he has tons of bills due, needs to pay his rent, still hasn't found a job, has run out of food, etc.? And if he hasn't found work within a few months more -- which is quite possible -- he'll be evicted from his home and his credit will be ruined from not having paid any of his bills for several months.
ETA: the point isn't that all of that will happen or is even likely to happen, but that a bank account represents some amount of time that the person can stay afloat while they're looking for work. It greatly increases the likelihood that they will find a new source of income before they hit the catastrophe point of being evicted and having their credit ruined.
It looks to me like you're ignoring the "reliable" bit in "reliable source of income".
Michael Anissimov posted the following on the SIAI blog:
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Kaj's commentary: if you haven't done so recently, do check out the SIAI publications page. There are several new papers and presentations, out of which I thought that Carl Shulman's Whole Brain Emulations and the Evolution of Superorganisms made for particularly fascinating (and scary) reading. SIAI's finally starting to get its paper-writing machinery into gear, so let's give them money to make that possible. There's also a static page about this challenge; if you're on Facebook, please take the time to "like" it there.
(Full disclosure: I was an SIAI Visiting Fellow in April-July 2010.)