The mailbox format most email programs use, is a bit of a packrat. Even after you tell it to delete messages, they're still in the mailbox file. Compacting folders is the process of actually removing these old messages from the mailbox file.

So unless the HP "compact" is doing something above and beyond that, which I wouldn't put past a company like HP, something else happened that your mother either forgot she did, or isn't owning up to. It's also possible that she's been infested with some pest that is messing with her settings.