DOMService API does not work as documented

The customer is trying to use the com.sun.java.browser.dom.DOMService API.
The method invokeLater(DOMAction action) should be
"executed asynchronously on the DOM action dispatching thread".
They have written a little example which is attached to this message.
         
Click on the button in the applet, then click on the button below the
applet. You will see that invokeLater is called on the AWT thread and
is called synchronously (i.e. the AWT event dispatcher thread waits
until the DOMAction is executed).
                                                                           
They tried this out on IE 6. When you trigger a DOMAction from outside the
applet (e.g. via JavaScript), the same thing happens: the calling thread
waits synchroneously until the DOMAction is executed. The same happens on
Firefox 1.5. All the tests have been run under jdk 1.5.0_06 on Win XP/SP2.
Another thing: the docs for invokeLater say: "It should not be called
from the DOMActionDispatchThread". Yet there is no way to find out
whether a thread is the DOMActionDispatchThread or not ( since the
Name is different on different platforms).