"the Android OS by default performs WiFi scans in the intervals of tens of seconds, even when the WiFi is turned off; the setting to disable background scanning when WiFi is off is buried in the advanced settings."
It looks like you can stop this from happening when the WiFi is off it just requires an extra step. I don't have an Android device so I can't really verify this.
When you set up android for the first time it gives you some text explaining what this is and how it works, and asks you whether you want to enable/disable it.
I'm not sure if this was ever a "default", but it is definitely part of the setup prompts now.
The option you are looking for is called "Keep Wi-Fi on during sleep" and it can be found under Settings -> Wifi -> Advanced on Android 4.3. This is the only device I can test with.
I advise turning it off unless you need it to be on, not only for privacy reasons but for battery life. I noticed an increase in battery life by turning that feature off.
On a Samsung Galaxy S5 running Lollipop (5.01?) it's under Wifi -> Advanced -> Always Allow Scanning.
With this turned off and GPS turned on (ie, not using Wifi to determine locations) I get a terrible reduction in battery life because all locations are done finely with the GPS chip. With all location services disabled I get much better battery life.
"the Android OS by default performs WiFi scans in the intervals of tens of seconds, even when the WiFi is turned off; the setting to disable background scanning when WiFi is off is buried in the advanced settings."
It looks like you can stop this from happening when the WiFi is off it just requires an extra step. I don't have an Android device so I can't really verify this.