The user wants to transmit the true/false response outside the jQuery object, so that the function can return it. There are situations were you really need the function to return something and not invoke a callback.
Even if the jQuery call is synchronous (i.e. 'async: false'), the example code above would not work, but it's true that your call must be explicitly specified as synchronous.
The correct way to do is to attach your jQuery object to a variable:
var obj = jQuery.ajax({ 'async:false', (...)
Then, at the end of your function, after the jQuery object closing parenthesis, add to your function:
return obj.responseText;