If you clone the OS on SD card, it has a Linux filesystem with permissions.
The /home/user folder has the owner "user". This name "user" is mapped to a number in the system, e.g. 1000. If your user on Ubuntu is mapped to the same number, then the folder will appear to be owned by you, otherwise not.
As root you can read everything. You can also change the permissions of /home/user and the files in there as root, so that other users can read/write it.

But as it is now, the /home/user on your SD card does not belong to the user that you are on your Ubuntu. That's why you get "permission denied".

If /media/disk is the mountpoint of the SD, you could do something like this as root:
Or you could use the graphical system tools of Ubuntu to create a new user with the same ID as "user" has on the tablet. You can see the ID of "user" if you enter "id" on tablet in the X-Terminal.