Yes, the library is in the firmware, but the OP doesn't post which version of the firmware that is installed on the card he is using, so if he hasn't flashed the card with the latest firmware, there is a chance that the firmware libraries are older than the ones found on the website.
Since the firmware libraries can be disabled through software, it is my opinion that it would be wise to download the latest libraries, when visiting the site anyway. I never said it was mandatory to download them.