So far, it appears the junction cookie issue was the culprit according to the IBM/WebSEAL AJAX documentation. By adding the following code to our ASP.NET page, the flytree control is working as expected.
protected void Page_Load(object sender, EventArgs e)
{
if (Page.IsCallback)
{
Response.Clear();
Response.ContentType = "text/plain";
}
else
{
Response.Clear();
Response.ContentType = "text/html";
}
}