jquery mobile iframe scrolling problems, when tapping on links - jquery-mobile

Question

I have encountered a weird issue with jQuery Mobile, where when tapping on a link in an iFrame and scrolling makes the persistent header in the parent HTML document move up and down with the scrolling. The interesting part is that this behaviour only happens when jQuery mobile has loaded a page in the iFrame. The full example can be seen here: http://www.cs.au.dk/~gedefar/jqm/parent.html (remember to load it on iPhone).
To the code and sorry for the lengthy example, but in order to show the problem I need three pages, parent.html, that contains the iframe, and two child pages, child_{1,2}.html that are loaded in the iFrame (with links to each other):
<div data-role="page">
<div id="header" class="header" data-role="header"
data-position="fixed" data-theme="c">
Foo Bar header
</div>
<div data-role="content">
<iframe src="child_1.html" />
</div>
</div>
child_1.html:
<div data-role="page">
<div data-role="content">
<h1> Child page 1</h1>
Go to child 2
<p>
Normal text, where the header is perfectly positioned when touching
here.
</p>
<p>
No problems below, when this page loaded directly in the iFrame. But loading
child 2 using JQM we get the scolling issues.
</p>
<ul data-role="listview">
<li>No link.</li>
<li>A link</li>
<li>No link</li>
<li>A link</li>
</ul>
</div>
</div>
child_2.html (no real difference to child_1.html, except the description):
<div data-role="page">
<div data-role="content">
<h1> Child page 2</h1>
Go to child 1
<p>
Normal text, where the header is perfectly positioned when touching
here and moving up and down after the first touch.
</p>
<p>
The problem is with list items below containing a link. For those the
header is not fixed. For the other it is fixed.
</p>
<ul data-role="listview">
<li>No link.</li>
<li>A link</li>
<li>No link</li>
<li>A link</li>
</ul>
</div>
</div>
What I find really weird is that the header is only moving when scrolling, if the first tap of the scroll is on a link on the child page. So any ideas here how to proceed? Or
Updated
I have tested the above scenario on different versions of iOS and it works perfectly in 7.0.3, but anything older than 7.0.0 the above problem is present. I don't have access to an Android phone, so I haven't been able to test it there.