Your accountant is correct. The trust laws do govern what trust can be a member.
If your child has a trust and receives income then your child would be taxed but you may be allowed the lower rate for your child.
Under the kiddie tax, children pay tax at their own income tax rate on unearned income they receive up to a threshold amount ($2,100 in 2015). All unearned income kids receive above the threshold amount is taxed at their parent's highest income tax rate. Depending on how much your child was to earn from the trust and the type of income would determine the actual tax advantage.
A trust is created when you (the grantor) transfer property to a trustee for the benefit of a third person (the beneficiary). Who is liable for taxes on income earned by a trust depends on who receives or retains benefits from the trust .
Trust income retained by the trust is taxed to the trust, while distributed income is taxed to the beneficiary who receives it.
Income earned by the trust can be in the form of interest, dividends, ordinary income, or capital gain. The character of the income stays the same when passed to the beneficiary.
If your child received earned income then that would not be under Kiddie Tax but if the Income was Unearned in character that would be under Kiddie Tax rules. This would mean you may still be paying tax on the amount over the threshold at your higher rate.