Quite simply: the statement is completely wrong.
A static member is just a member that is not associated with an instance of a class, but with the class itself (rather: with its class object). And unlike "normal" objects (class instances), class objects will not be garbage-collected as long as the class is loaded, because they don't go out of scope or become orphaned. So far, so correct.
However -- and this is the important point -- every Kindlet is instantiated in its own, isolated, classloader. All of the classes and instances of that Kindlet only ever live inside that classloader. And when the Kindlet is terminated - poof! - the class loader and everything that was "produced" by it is discarded and can be garbage-collected. Unless there are memory leaks inside the JVM implementation, this is no problem at all, and the statement simply shows a lack of understanding of how the class loading mechanism works and is implemented on the Kindle. (more technically, we're talking about ClassLoader delegation and isolation... ask your favorite search engine about it).
Admittedly, this is not the easiest topic to wrap your head around, but the Kindle uses the same technique as any other "application server"/"web container"/whatever you want to call it. If it didn't work, half of the WWW would constantly be crashing because of OOM errors
That said, yes: the Kindle does have rather severely limited memory, and if you aren't careful, it's relatively easy to hit the roof. But the problem that you're referring to just isn't a problem.