Input Validation is the outer defensive perimeter for your web application.
In suggesting that users are untrusted, we imply that everything else is trusted. Users are just the most obvious untrusted source of input since they are known strangers over which we have no control.
You may print some message after sending mail optionally.
Each of these allies have their own perimeters which may or may not trust ours. As noted in the Introduction, we trust nothing and nobody.
The common phrase you will have seen in PHP is to never trust “user input”.