Oh, don't get me wrong. I completely agree that they should quit pretending and build their 'webapp' using actual web technologies. Wrapping a big chunk of java in a thin HTML shell is about as 'web based' as putting a win32 executable on your server and claiming that it's 'web based' because users can download it over HTTP.
My point was just that, if somebody is depraved and/or forced enough to use java applets on the desktop, java's ability to be equally frustrating across all major platforms and some minor ones is a fairly major advantage. Even Flash doesn't have quite the same breadth, and sucks at least as much if not substantially more.
Using a JVM on the server is substantially more defensible; but is also largely invisible to the poor users.
(At work over here, we have some very expensive-and-fancy-when-they-were-new heating/cooling control systems with java based interfaces. For the moment, carefully maintaining IE6/Java 1.4 is more attractive than shelling out ~30k per unit to have the vendor swap the boards, no software update here, everything burned into hardware; but it hasn't created warm feelings about java.)