Device is Mounting as Read Only (Can Copy Files as Root)
Figured it out (thanks to everybody who helped jog the brain a little bit).
Because usbmount is doing the automounting, this is where the problem lay. And, conveniently enough, usbmount provides a configuration file for managing how a drive gets mounted. In order to manage this, open /etc/usbmount/usbmount.conf.
There is a line in the file that looks like this:
Add the uid and/or the gid that you would like the device to mount as.
Now, my drives automount correctly every single time.
The accepted answer does not work for me (Ubuntu 12.04)
/etc/usbmount/usbmount.conf and changing the line starting with
,uid=1000,gid=1000, did the trick for me.