You aren't providing any numbers, but let's assume the deduction for state income tax is $500 and the distribution to the beneficiary was $10,000.

Your choice on the front of the 1041 for total deductions is either $500 tax and $9,500 DNI, or $0 tax and $10,000 DNI.

Where is the double benefit?  The trust pays the same tax, either way.  If it chooses not to claim the allowable deduction for state income tax, the beneficiary needlessly pays tax on $500.  Something seems to be going on here, are there other issues between you and the beneficiary?