The withdrawal should not have any effect on the earned income credit. However, it is possible that the investment income earned by the trust could interfere with the EIC. They should also get full credit for the tuition deduction and or education credits related to those expenses.
It depends somewhat on how the trust is structured and how the distribution was accounted for on the trust tax return. However, what you stated is basically correct - the trust's income that is attributed to her is what counts for EIC purposes. If the distribution was a corpus or principal distribution, it would not affect the EIC calculation.