The "condition" to display the "Re-use existing tables" depends on a hard-coded number of expected core tables. This leads to a number of use cases and problems:
SQLSTATE[42S22]: Column not found: 1054 Unknown column 'idsite' in 'field list'
On second thought, creating the missing tables isn't really adviseable as there may have been other schema changes (between the current db version and the installed version of the software). Exercise caution when advising people to delete config.ini.php, and re-run the installer to regenerate config.ini.php.
(In ) fixes #2046 - increase base table count; fix spurious table deletion