It turns out that this apparent bizarre calculation is correct. It is due to New York's non-linear way of looking at the NYC School Tax Credit (line 69, IT-201), and the - NYC school tax credit (rate reduction amount) (line 69a, IT-201).
It is easier to consider the two credits as totally separate, for two separate, inconsistent circumstances.
The NYC School Tax Credit:
If you are a New York City resident or part-year resident and marked the No box at item C on the front of Form IT-201 indicating that you cannot be claimed as a dependent on another taxpayer’s federal return and you are filing status [anything other than MFJ] (and your income (see below) is $250,000 or less), determine your credit using Table 1 below if you were a full-year resident or Table 2 below if you were a part-year city resident. See IT-201 Instructions.
Clearly, the income is more than $250,000, so no credit allowed.
However, the rate reduction amount credit is calculated quite differently:
Calculation of NYC school tax credit (rate reduction amount) for single and married filing separately
If the income is between $ 0 and $ 12,000, then credit is 0.171% of taxable income
If the income is between $12,000 and 500,000 then the credit is $ 21 plus .228% of the excess over $12,000
Clearly, the rate reduction amount credit is available up to $500,000, which both spouses are eligible for.
Basically, the school tax credit cuts off at $250,000 while the rate reduction amount credit cuts off at $500,000.
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