NTFS vs FAT32 should not affect anything.
The usual cause of this (other than a lack of administrator privileges) is some kind of security software that sees a program trying to write to a different drive in the manner that the Windows 10 Media Creator Tool does as malware (or a virus, what-have-you). The reason that copying the file directly to the drive and running it from that drive solves the problem in these situations is that it removes this suspicious cross-drive behavior. This is also the reason why many users report temporarily disabling their security software as a solution to the problem.