Right (based on the facts you have stated here).
The earnings portion of a 529 distribution is only subject to tax if all or any part of the distribution is used for non-qualified expenses. The person responsible for filing the tax return and paying the tax (if any tax is owed) depends on who received the distribution.
It depends on whether or not there were taxable gains realized when the UTMA account was liquidated. If taxable gains were realized, the account administrator should be providing the required tax form (a 1099 of some sort) in the next several weeks.