<p>There are two ways this UK student could be a citizen.</p>
<ol>
<li><p>Born in the U.S…citizen regardless of the citizenship of her parents.</p></li>
<li><p>Born abroad with at least one parent who is a citizen.</p></li>
</ol>
<p>To be honest, it sounds like the family has really not lived in the U.S. for 30 years…at least. OP says that is when the home was purchased.</p>