So,

Solaris has it's ways ... When working with zones, the default configuration for directories in zones is ro-mode only.

inherit-pkg-dir:
dir: /lib
inherit-pkg-dir:
dir: /platform
inherit-pkg-dir:
dir: /sbin
inherit-pkg-dir:
dir: /usr
This means that if you install/boot/configure your zone, when you log in, you will not be able to install custom software which puts files/directories in /usr for example.

To be able to write fully to all paths from your zone, you need to remove these 'restrictions'. I use the word restrictions carefully because packaging should happen from the global-zone.

Be sure you configure this _before_ installing your zone!

zonecfg:YOUR_ZONE> remove inherit-pkg-dir dir=/lib
zonecfg:YOUR_ZONE> remove inherit-pkg-dir dir=/usr
...

Now you can fully write to every directory in your zone.