I have seen the 'case sensitivity' issue before, usually with software developped for multiple databases where the other database (say SQL Server) is case sensitive. Almost always the same situation (a software house with a canned project). I don't like it, but it is your coding headache.
As for the customer worry, why not just use a definition export as part of your installation process. Create the objects with case sensitivity, export the definitions (ROWS=N) and use that file for installation. If the client changes the installation procedure or objects afterward, they violated your support aggreement, yada yada yada.
As for the database, the Instance name may be case insensitive (depending on platform, release etc.) but the Oracle doesn't use databases the way other RDBMSs do. A SQL Server instance contains multiple databases which contain schemas. Oracle instances just contain schemas. SQL Server databases can be case sensitive but there is no corresponding object in Oracle.
Joseph R.P. Maloney, CSP,CDP,CCP
'The answer is 42'