I’ve noticed the use of this, perhaps vogue, expression, to vet as in: vetting the manuscript or It might be vetted by the IRS etc. The reason I refer to vogue expression is because I’ve noticed the usage more in television news and periodicals than in books. I was familiar with the meaning but not the etymology; sometimes we don’t pay attention to the etymology because we know the meaning.
I was surprised to find out that it is nothing more than a verb formed from the noun “veterinarian”, and originally meant to examine or treat as a veterinarian does. More recently(approximately 100 years) it has come to be used to mean any careful inspection of a document or manuscript.