Here is my friend Freya doing an almost silent purr. So different from the loud purr by Tilly which you will find on my Youtube cat signals playlist. I couldn't video a silent purr because listeners or viewers would simply assume that I had turned the sound off.
Some of us purr very very loudly. Some purr moderately. And some purr so silently that our dumb humans cannot hear us and think that we don't purr at all.
If they looked more closely they would see the slight movements in the chest. Some humans put their ear close to our bodies to see if they can feel the vibrations. They usually can.
Luckily I purr moderately. I feel that the loud purrers are giving their humans too much feed back.
If I was unlucky enough to be a silent purrer my human would never know I was doing it. Because if she put her ear close to my body I would simply swipe at it...
You have to stop them taking liberties.