A company doesn't need to know they are under compensating for a role from a third party. They'll find out by the quality and number of applicants pretty fast. I've seen this in practice directly when we couldn't hire for certain roles, raised the range, filled the spots.
On the other hand, to know that other companies are paying lower and still able to deliver roughly the same work is harder unless you know how much they are paying.
On the other hand, to know that other companies are paying lower and still able to deliver roughly the same work is harder unless you know how much they are paying.