That statement is a bit hyperbolic, but making 4th quarter state estimated tax payments in January might serve to reduce AMT (not eliminate it altogether), because tax payments are not deductible when the AMT is calculated. However, 4th quarter state income tax payments are not generally due until January 15th anyway. So if you pay them on the normal due date, there would be no effect; if you normally paid them before the due date, delaying a bit might cut AMT slightly. However, if you owe AMT the following year, they would still not be deducted.