I'm not looking for a workaround; I'd like an explanation. Most of the links I found through Google just tell me that the file limit is 4GB, but not why.
I am aware of the explanation by Wikipedia: http://en.wikipedia.org/wiki/File_Allocation_Table#FAT32
But this still does not go into detail about why. (What does SCANDISK have to do with it?)
Maybe then I will understand whether it's possible to overcome the 4GB file size limit.
Because FAT32 stores 32-bit file sizes and the maximum you can store in 32 bits is 2^32-1 ~= 4.29e9. 2^32-1 bytes = 4GB - 1 byte.
(This is, in fact, explained in the Wikipedia article.)