If I put the following method in my Java service class:

private String fruitName() {
 return 'banana'
}

I get the following in my AS3 service proxy object:

public function this$2$fruitName(resultHandler:Object = null, faultHandler:Function = null):void {
    if (faultHandler != null)
        callProperty("this$2$fruitName", resultHandler, faultHandler);
    else if (resultHandler is Function || resultHandler is ITideResponder)
        callProperty("this$2$fruitName", resultHandler);
    else if (resultHandler == null)
        callProperty("this$2$fruitName");
    else
        throw new Error("Illegal argument to remote call (last argument should be Function or ITideResponder): " + resultHandler);
}

It's fine to just ignore this when your method only returns a String, but if you're returning an object that doesn't exist on the AS side then this creates a compilation error.

Please ignore private methods when generating service proxies.