Unless you have the schematic of the board, or make a bit of reverse-engineering, you can't assume there isn't something else than just the LM2576 connected to the input supply. There are at least the input capacitor (which has a rating most likely well under the 40V), and there may be some additional monitoring circuitry, or protection circuitry on the board too.
So the only thing you can trust here (assuming you can trust something from a cheap ebay/aliexpress product) is what it tells you in the description: 12V.
Moreover, the battery voltage in a car is much more unreliable than what you seem to think. It is not guaranteed to be within 12-15V. It can actually go up to 100V peak during load dumps. So I would choose components that can take at least 20-30V for normal operation, coupled with some beefy protection that will be able to clamp or disconnect any higher input voltage, up to 100V. This could eventually be implemented with an intermediate circuit between the battery and the LCD board you selected.
There are a lot of documentation material available about automotive load-dump protections. Here are a few application notes, for example: