Absolutely a 'continental' thing to do.That is the normal thing to do over here - drive through any residential area early morning and you will find lots of pillows and duvets hanging out the window.
It's widespread in Germany and Switzerland and, having lived there for years, I'm in the habit of doing it as well - not out the window, but once a week if I manage to get a reasonably dry day , I'll hang all the duvets out on the line to air them.
Dust mites don't like cool fresh air.
Keep a written log of when this person called you, the fact that she didn't wish to give her name or number, what was complained about, who you contacted in relation to the complaint (other neighbours, your tenants etc.) with dates and details just in case she decided to contact the PRTB. At least that way you have a written record of the complaint and your response to it.I can't even contact the complainer as she rang on a private number and refused to give me her name so I can't let her know I've acted on it.