Add capabilities via plugin for another plugin

by

There’s a couple issues here:

  1. is_singular() will return false if the function is called before the WP_Query object is set up
  2. user_has_cap hook fires early and often – and before WP_Query is set

We know that the WP_Query object is set at the wp hook, so you can use that action hook to add a filter for user_has_cap. 

add_action( 'wp', 'sqms_wp_action' );
function sqms_wp_action() {
  //* Since the WP_Query object is set, is_singular() should work properly
  if ( ! is_singular( 'sqms_payne_dealer' ) ) {
    return;
  }
  add_filter( 'user_has_cap', 'sqms_user_has_cap_filter' );
}
function sqms_user_has_cap_filter() {
  //* No need for is_singular() check
  //* Rest of code unchanged
}

So, most of your code was correct. It was just executed in the wrong order.