That's because for FAT, erasing a file just means flagging the file allocation table entry as deleted, which normally makes the filesystem software put the linked list of sectors pointed by this entry back to the free sectors list (I'm pretty sure I am wrong on some details here, but I think the general idea is correct).
In other words, when you "delete" a FAT file, you are not even erasing a whole directory entry, you just merely flip one bit in that entry.
The data blocks get actually "erased" when they are reused by the FS software.
Recovery of basic deletion is therefore pretty much guaranteed as long as you didn't write something else on the disk.
What the author is talking about is more "serious" deletion, sometimes called "shredding" [1]. To actually erase the data from the disk, you use software that overwrite your file with random data before deleting it. This is supposed to work if the filesystem is as clever as FAT - that is somewhat dumb (but so simple that SoCs such as ARM Cortex Ax can boot from them directly).
SDs and SSDs add another challenge because they constantly lie to the filesystem software; they have their own inner controller mainly to manage bad sectors and do wear-leveling, so when the FS requests to fill a sector with zeros, they might say "ok" but actually just remap the sector internally to another empty sector. So the data is still somewhere on the chip, and an evil scientist with lots of pointy probes can in theory read them back.
[1] https://linux.die.net/man/1/shred