If the objection is to the technology: Lots of companies use special techniques to avoid creating a paper trail.

It's called "phone calls" and "talking privately". Using that to do bad stuff is bad, but conducting certain matters in a way that doesn't leave a paper trail is not by itself objectionable. I don't know any workplace that tries to ensure all communications leave a paper trail (though I did have a Facebook friend who insisted he only worked at such places, which must be false, since he's employed).