It is not modding. You are not modifying any files at all. You are just copying them, which is what Microsoft allows with the "Copy" and "Move" functions.
Getting the XBLA game unmodified from the Internet is the same as getting it unmodified from your friend.
On the other hand, if you were modifying the XBLA files from trial to full without paying, then yes, this is modding, and this requires a modded console. Microsoft does not want this.
Correct me if I'm wrong, but xbox uses it's own file system to store content which is not readable normally in the PC. Once you format the USB memory stick in Xbox to use it, Xbox changes the file system.
I didn't know that you can put Xbox content on a normal FAT/FAT32/NTFS. That's strange.
That's why I thought it should be somehow modified.