(* A JRE doesn't really qualify as a "fat client". *)
It ain't skinny.
The biggest factor of a "fat" client is downloading programming code to the client. IOW, depending on the client executing app-specific code written in a Turing-complete language.
My HR benefits were available on some Java applet written by (or for) a fairly large benefits mgmt company. It took about 20 minutes to download via modem to check on my HMO status. F that!
(* HAVING to run Windows, now THAT's fat. *)
But that is not a remote-app issue. IOW, besides the point.