1) Wikipedia doesn't have 5 billion unique visitors (there are only 1.6 billion internet users in the world). And they only put up banners asking for money when they need it, not all the time. So both variables in coming up with the "$.00124/visitor" estimate are incorrect.
2) Tax deduction does not make something cost-free. For most people, a donation saves them nothing (since they use the standard deduction) but even for those who itemize, it only saves them the tax they would have paid on that income, not the income itself.
3) Tipping doesn't have to create price uncertainty. As someone who has tried the donation model, it's clear that if you set the price of a donation (such as placing a banner that says "Give $5 now"), that's the exact amount that 90% of people will donate. So in essence, you do get to influence what the perceived value of your site is worth.
4) The article claims that in order to orgs like NPR to succeed on the donation model, they have to have federal grants and corporate sponsorship, etc. But this argument ignores the low barrier to entry (and low cost) of online content; it's not a valid comparison.
5) The article also mentions that those orgs can succeed because they offer physical goods and imply scarcity, but there's no reason that a donation-accepting site could do those as well.