Because it’s mounted.
The ‘dirty’ bit is set as soon as the filesystem is mounted, and cleared as soon as it’s unmounted.
In general, this could be somewhat dangerous, as the tool apparently assumes that you will only be using it on an unmounted filesystem. (Fortunately, changing the label of a FAT volume only touches a single dedicated directory entry so it is unlikely to conflict with other filesystem operations or cause corruption, but since the tool clearly hasn’t been designed for that, it is best to not use it this way.)
Some other Linux filesystem drivers have an ioctl which allows tools to change filesystem metadata on a mounted filesystem, e.g. btrfs/xfs have FS_IOC_SETFSLABEL. Others were specifically written to allow the label to be changed from under their nose, e.g. ext4 allows e2label to do this. But the vfat filesystem driver currently has neither of those.