That seems to be a misconception.
The usage frequency of simple words is a powerful tell.
I can understand the nuance of your assertion, but looking at the data returned by these results suggests it's not really all that powerful at all.
There are so many people that write like me apparently, that simple language seems more like a way to mask yourself in a crowd.
You can definitely mask writing style. If you can do that only by using simple words, I am not so sure.
Indeed, some writing styles make frequent use of words like "that" and "just".