You could try this:
Put back the onclick event, but in the JavaScript, add this as the first line of the checkForm function.
It goes just below this line:
function checkform(form) {
You could also comment out line 113 of the subscribe form snippet:
Change this:
$modx->regClientStartupScript($jsPath . $jsFile);
to this:
// $modx->regClientStartupScript($jsPath . $jsFile);
When you change the form to remove the onClick event, be sure to remove the "return false" part. IOW, change this:
<form class="sbs_register_form" action="[[~[[*id]]]]" method="post" onsubmit="return checkform(this); return false;">
to this:
<form class="sbs_register_form" action="[[~[[*id]]]]" method="post">
That should let you test the action without the JS.
My guess is that your problem is caused by the cache (either MODX's or your browser's). JavaScript tends to hang around in the browser cache.