After more investigation into this, I found out that if there is only one textbox in a form, the enter key will trigger a submit. If there are two or more, the enter key does not trigger a submit. This seems to be a natural behavior of HTML, not specific to any browser.
So, basically, when someone adds the onkeypress support at the textbox level, we would have to avoid adding that support if there is only one textbox on the form at this will trigger a dual submit. Is that your understanding as well on that issue?