There are only two possible ways a student can justify a claim to providing more than half of their own support.
1) They have a W-2 job or are self-employed and their earned income is of a sufficient amount to support a claim of providing more than half of their own support.
2) They are the "PRIMARY" borrower on a qualified student loan, and funds distributed by the lender during the tax year are of sufficient amount to support the student's claim to providing more than half of their own support.
That's pretty much it. All other sources of income are considered 3rd party support and do not count for the student providing more than half of their own support. For example, scholarships, grants, 529 or Coverdell account withdrawals are considered 3rd party sources of income.
Now I don't know this for a fact about an inherited IRA, but since that money was not earned by the student, I would expect it not to count either.
Take note also that if the student is under the age of 24 on Dec 31 of the tax year "AND" meets the other four requirements, there is NO LIMIT on how much the student could have earned during the tax year either. The student could ahve earned $500,000 and it wouldn't matter, so long as the student did not provide more than 50% of their own support. The parent's would still "QUALIFY" to claim the student as their dependent.
