Doesn’t even necessarily need internet altogether
i suppose that can be construed as a technically correct statement but it is functionally false. the entire function of wifi is to access the internet (wirelessly). its kind of like saying a cellphone doesnt need a cellphone service. true it will still light up and make keypad tones but it cant perform the function for which it was created (like atheists).
dial-up, cable, dsl are the main technologies to access the internet.
wifi is a technology to broadcast ones internet connection (once accessed via the above), wirelessly and locally so that it can be accessed with a nearby wireless device.