I think nearly all bug reporting options should be globally controlled. This could be accomplished for severity by the changes to bug_report_page.php and bug_report_advanced_page.php outlined below as well as adding the appropriate, corresponding global variables to config_defaults_inc.php (e.g: $g_set_severity_threshold).

CHANGE FROM:
<!-- Severity -->
<tr <?php echo helper_alternate_class() ?>>
<td class="category">
<?php echo lang_get( 'severity' ) ?> <?php print_documentation_link( 'severity' ) ?>
</td>
<td>
<select tabindex="3" name="severity">
<?php print_enum_string_option_list( 'severity', $f_severity ) ?>
</select>
</td>
</tr>

CHANGE TO:
<!-- Severity (if permissions allow) -->
<?php if ( access_has_project_level( config_get( 'set_severity_threshold' ) ) ) { ?>
<tr <?php echo helper_alternate_class() ?>>
<td class="category">
<?php echo lang_get( 'severity' ) ?> <?php print_documentation_link( 'severity' ) ?>
</td>
<td>
<select tabindex="3" name="severity">
<?php print_enum_string_option_list( 'severity', $f_severity ) ?>
</select>
</td>
</tr>
<?php } ?>