The following is the Change I did based on krzysiekmat solution.
To solve this issue you need to change three files user-change_password.php, user-profile.php and user-change_email.php. For example in twitter_bootstrap\user-profile.php. The change is at Line No. 19
Before change
<fieldset>
<legend><?php _e('Change your e-mail', 'twitter_bootstrap') ; ?></legend>
<div class="clearfix">
Move the <legend> tag to the Line No.15 Just below '<?php twitter_show_flash_message() ; ?>' tag.
After change
<?php twitter_user_menu() ; ?>
<?php twitter_show_flash_message() ; ?>
<legend><?php _e('Change your e-mail', 'twitter_bootstrap') ; ?></legend>
Do the same changes for user-change_password.php and user-change_email.php files. Note that the line numbers may change in these files but the solution is same. Move the <legend> tag.
Message me if this is not working.