Preventing 'submit' button from being double-clicked causes side effects?

I am trying to prevent a SUBMIT button from being clicked twice quickly in succession. 
My page has form fields with validators and the button.
One of the fields is a radiobutton field that does a 'postback' and makes other fields visible/invisible depending on which radio in the set was clicked.
So I replaced my submit button by:
<asp:Button runat="server" ID="ButtonSubmit" Text="Submit" OnClick="ButtonSubmit_Click"  OnClientClick="if (!Page_ClientValidate()){ this.disabled = false;  return false; } this.disabled = true; this.value = 'Submitting...';" UseSubmitBehavior="false" />
But to my surprise (I spilled my latte) the new behavior of the page is that if you click on one of the radios that does a postback, the 'submit' routine fires as well!
Why is that?  Is there a way to avoid it? 
I have to clean up my latte now off the rug ...