Why can't I update the fields in a table created using Application Composer? 

Ensure that the access group security is enabled for you to access the custom object's data.

Access groups provide you with access to custom object data. After the admin enables access group security for you for a custom object, you can work with it just like a standard object.

If the admin configures both owner and access group security, then you can view data from both your owner management chain and from the access groups to which you belong.