Critically, it's an A implies B but not necessarily vice versa situation
One can easily have thinking without writing; many of the trades barely require literacy to apply ingenuity and creativity.
But — until recently — one could not do writing without thinking. it was usually easier to actually do the thinking first, than to fake it and still do the writing.
Good writing was a low-error-rate* sign that "thinking has been done"
*Some exceptions apply, of course