WiFi as a term does not specify local multiplayer or online multiplayer. The latter appears to be what he was referring to though.
Actually it does. You need a wifi connection to play online, but you don't to play local. If you did, then you wouldn't be able to play local when not near a wifi router.
So if you decide to play a local multiplayer game against someone else does your 3DS not establish a WiFi connection to the other device? If not, then please explain what kind of magical transport method your 3DS utilizes.
WiFi is a local wireless transport method. In order to have Internet access it has to bridge some other connection to enable itself to connect to the web. I'm assuming Nintendo is causing some confusion by their use of "Nintendo WiFi connection", however WiFi as a technique is strictly local and does not magically establish access to the Internet on its own.
If you still don't believe me then please do go and have a look at the definitions of the different IEEE 802.11 standards.