Think the check is looking at global settings for the DB server ... those found in my.cnf. That's where one finds file format setting for Barracuda. It's NOT looking at the settings for the DB itself. The assumption is that moodle server is on/using a DB server to which the OP has superuser credentials. Although in doing the script located in moodlecode/admin/cli/ for compressing tables does have an option to show the SQL ... which shows alter commands.
Seems to me that even if remotely hosted on shared, the OP should have access to alter their own databases.
Before I get into the installer, I create the database manually and while doing that one can set character set/collation. I've even discovered that one could partially fill in the DB variables of a copied config-dist.php file to a config.php file and be able to use the CLI scripts prior to actual installation/upgrade.
Qualifications for above response ... none ... not a DB admin/expert ... but do have to work through problems many times.
'spirit of sharing', Ken