From your own link: The Wii console is only compatible with SD Cards that are 2 GB (Gigabyte) or less. Cards with a capacity higher than 2 GB will likely not work with the Wii console.
Obviously outdated info since 4.0 allowed the 32 SDHCs [and it doesn't even reference anything about WiFi enabled saves], so I repeat, which update opened that up? 'cause the current 4.2 system update isn't allowing it as of a few minutes ago, so it had to have been a previous system update.
Particularly when did this became outdated? http://www.nintendo.com/consumer/systems/wii/en_na/data.jsp#SDcopy
To copy Save Data to an SD Card (...) Please note that while most game save files can be copied, some titles -- particularly those that have online play -- may not allow for the copying of save files to an SD Card.