Index: wp-admin/includes/class-wp-posts-list-table.php
===================================================================
--- wp-admin/includes/class-wp-posts-list-table.php	(revision 18596)
+++ wp-admin/includes/class-wp-posts-list-table.php	(working copy)
@@ -890,10 +890,12 @@
 
 	<?php foreach ( $flat_taxonomies as $taxonomy ) : ?>
 
+		<?php if ( current_user_can( $taxonomy->cap->assign_terms ) ) : ?
 			<label class="inline-edit-tags">
 				<span class="title"><?php echo esc_html( $taxonomy->labels->name ) ?></span>
 				<textarea cols="22" rows="1" name="tax_input[<?php echo esc_attr( $taxonomy->name )?>]" class="tax_input_<?php echo esc_attr( $taxonomy->name )?>"></textarea>
 			</label>
+		<?php endif; ?>
 
 	<?php endforeach; //$flat_taxonomies as $taxonomy ?>