NY begins the tax return with the federal AGI. Form IT-196 begins with the federal itemized deductions. Even though there is no state deduction, there was a little on the federal. The addback should match what was allowable on the federal Sch A.
The credit is allowed when no other LTC expenses are claimed so this clears the path for you to take the credit.
Your logic makes sense but the program follows state rules.
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