Form tag won't enclose elements inside a table

I've run into a curious problem; I've got a form inside a <tr>, however the form refuses to wrap any tags inside it. I've made a quick JSFiddle here to play around with. Firebug reports that the form isn't wrapping anything:

The <form> element is greyed out and not wrapping anything. The HTML for this test is below

<table>
    <form>
        <tr>
            <td>Input</td>
            <td>Another input</td>
        </tr>
        <tr>
            <td colspan="4"><span>Other stuff</span></td>
        </tr>
    </form>

    <tr>
        <td>
            Rows not affected by the form
        </td>
    </tr>
    <tr>
        <td>
            Rows not affected by the form
        </td>
    </tr>
</table>

As can be seen, the form holds two trs in the written markup. I read here that this is invalid, so my question is can I create a form that holds two or more trs and an arbitrary amount of other elements inside a table? The table has other rows in it not associated with the form, so putting a <form> round the entire table is unhelpful, although seeing as the other rows won't have any inputs for the form (POST request), I suppose a form could be put around the entire table.

Which is a better solution; whole-table wrap, or a working fix for just enclosing the needed rows in a form tag? I know I could put a table inside a td > form, but then the column widths wouldn't be the same in the nested table, which is why I came to ask this question.