It's MOSTLY true, but there are exceptions, primarily in largely radio-dead rural environments, and with the application of high-gain sector antennas.
A high gain antenna concentrates the radiated radio power (within local legal limits, of course) to a particular physical area, and also has the same amplifying effect on a signal originating from that particular physical area, even if the antenna radiating that signal is a standard low-gain omni-directional antenna.
This only works in relatively radio-dead (but tree-free) rural areas because the antenna will also pick up any competing noise source in its "beam." I emphasize this point since many people jump to the conclusion that it can be applied anywhere, and that's not even close to true. I have personally tested my system (16 dB 2.4 GHz sector) and got acceptable performance to 435 meters before I ran out of test range, going to an ordinary (crummy) wifi antenna in a laptop, and wifi in a cell phone. My actual production application for this system is more in the 200m range, feeding athletic fields and backstopped by a hill with no houses or transmitters on it. An online acquaintance has a ski-area setup with mountaintop sectors that typically operates to normal hand-held devices at 1-km ranges - but I reiterate that this only works because it's the only thing in the area operating on those frequencies, and there are no trees to stop them.
In general, in the real world, if you want wi-fi over whatever you mean by a "1km distance" (a 2km circle, a 1 km square, etc.) you build a backhaul (preferably fiber, or via point-to-point links on frequencies you will NOT be using for WiFi) and you hang a large number of access points which are serving a much more reasonable radius each, such as 100m (in a clear field) or 30m in urban environments. Or you skip wi-fi entirely and head into 3G/4G cell-phone data schemes.