I do not know, it works for me.
What I tried is getting the example from your link (so streaming.radionomy.com/JamRock), and wrote a downloader for it:
actually it is desktop code (Socket, FileOutputStream, System.out), but I really believe that Java ME behaves similarly.
Socket s=new Socket("streaming.radionomy.com",80);
os.write("GET /JamRock HTTP/1.0\r\n\r\n".getBytes());
byte b=new byte;
FileOutputStream fos=new FileOutputStream("test.mp3");
fos.write(b, 0, l);
The result was playing well on a Nokia N8 (I have no Asha devices, so that may be still different).
The only tricky thing is that InputStream.read reads some (kilo)bytes only, so passing a few megabytes array to it does not mean that you get few megabytes of data. DataInputStream has a readFully method, just I did not want to mix that here.