I would say by looking at this, the reason you are having this issues is the Download and Public folders are different mounts.
In my case, I am running a bluering and here is my mount:
/dev/root on / type ext3 (rw,noatime,data=ordered)
proc on /proc type proc (rw)
devpts on /dev/pts type devpts (rw)
sys on /sys type sysfs (rw)
/dev/md3 on /var type ext3 (rw,noatime,data=ordered)
/dev/md4 on /shares/internal type ext3 (rw,noatime,data=ordered)
usbfs on /proc/bus/usb type usbfs (rw)
Did the following on my rig and can reproduce the issue.
sudo su -
mount /dev/md4 /tmp/test
mv /internal/shares/folder/XXXX /tmp/test/XXXX
This would be the equivelent of mv /shares/internal/folder/XXXX /shares/internal/XXXX
(Still same disk, only one directory up)
This does result in the file being copied instead of moved. The OS can not tell they are one in the same so it just does what it normally would when copying the data to another drive, cp then rm. The only solution I could see for this would be to take samba into your own hands and edit the conf file so all your shares are in one root dir (/internal/shares/ in my case). I do not use the webif at all and only edit smb.conf by hand, maybe this is why I never experienced the issue.