I don’t know why the scrollbars don’t show up in any other browser but in a mobile browser the phone zooms out much too far by default. However you can easily fix it by adding the following tag to your page header.
<meta name="viewport" content="width=device-width, initial-scale=1.0;" />
Here is a full sample:
<!DOCTYPE HTML>
<html>
<head>
<title>I love titles!</title>
<meta name="viewport" content="width=device-width, initial-scale=1.0;" />
</head>
<body>
...
</body>
</html>