This is what I came up with to display the category, or rather a custom taxonomy, of a single posttype page of use in a breadcrumb. The taxonomy I used is ‘smg-logo-brand’ and the terms slug where ‘kcrg’, ‘the-gazette’ and ‘sourcemedia.’ I compared the terms associated with the post to that in the URL to determine which term belonged in the breadcrumb.
if (!is_tax() && get_post_type() == 'smg-logo' && has_term( array( 'kcrg', 'the-gazette', 'sourcemedia', 'other' ), 'smg-logo-brand' ) ) { $terms = get_the_terms( get_the_ID(), 'smg-logo-brand' ); foreach ( $terms as $term ) { if ( strpos( $_SERVER["REQUEST_URI"], $term->slug ) !== false) { $breads['terms'] = '<a href="/logos/'. $term->slug . '/">' . $term->name . '</a>'; } } }