Well, I broke down and spent the morning investigating my tax situation, which was rather confused at the end of last year. After some burrowing, I found that TurboTax was surprisingly right after all. Scholarships and fellowships that are reported on Form 1098-T rather than Form W-2 count neither for "earned income credit" (on Schedule M) nor for IRA purposes.
As regards Schedule M, which covered 2009's "Making Work Pay" credit, the "Earned Income Worksheet" line 4a specifically subtracts scholarship income: so people who rely solely on fellowships for their income are not eligible for earned income credits.
Finding out eligibility for Roth IRAs took considerably more digging, because on some portions of the 1040A instruction sheet, it says that scholarships count as "earned income." If you look at Publication 590, it says under "What is compensation?" that "Scholarship and fellowship payments are compensation for IRA purposes only if shown in box 1 of Form W-2." You can only contribute to an IRA if you have a non-zero "compensation."
So there you have it. This is not official tax advice, but you should look at the linked forms and draw the same conclusions that both TurboTax and I did. I'm glad the situation is clearer now, though of course I wish our tax system weren't such a mess.