I spoke to WDZ about this possible solution to the caching in the shoutbox, and he said he wouldn't be implementing this idea because he wants some things (such as images, which many people use as attachments) to be cached. Otherwise it's really a waste of bandwidth when people are constantly re-downloading images.
I guess it is possible to only implement this idea for files ending in specific filetypes... but don't bet the house on it because it is WDZ after all