Do you have a multimeter? Put it on Voltage, at a setting > 14V. Red wire/clip to red (+ terminal), black wire/clip to black (- terminal) connection. If the battery is below 12.6V with the engine turned off, it is starting to give. If between 12.6V and 12.8V, the battery is likely fine. And, as I posted earlier this morning, the "eye" (a built in battery tester) is not the most reliable of indicators once the battery has been put into use. But the dealership probably has a more sophisticated battery tester they can verify it with.