Clarifying AngularJS theory snippet from Tutorial

This does indeed refer to scope inheritance and its (often not straightforward) consequences. In case you haven't seen it already, here is a great write-up: Understanding Scopes

It can get much more tricky than what you think :) Especially (as the tutorial mentions) for large, real-world apps, where different teams work on different parts of the app or where certain parts remain untouched for months.

To show but a very simple, "realistic-ish" example (which again is nothing near as complex as a large app):

Imagine that you are starting your own business; an e-shop. You want to start small, so you only have phones and tablets for now.

All you need is a basic layout - a header, a nav-bar and your content area:

My Cool e-Shop
----------------------------
[Phones]   [Tablets]
----------------------------

<CONTENT HERE>

You set up two routes - one for phones, one for tablets - and decide to encapsulate each page's content as a component-like directive. E.g. the #/phones route will have a template like <phone-list></phone-list> and the phoneList directive will look like this (unfortunately you had never heard of isolate scopes):

.directive('phoneList', function phoneListDirective() {
  // DDO
  return {
    template:
        '<h2>Phones</h2>' +
        '<ol>' +
          '<li ng-repeat="phone in phones">' +
            '<b>{{ phone.name }}</b> (OS: {{ phone.os }})' +
          '</li>' +
        '</ol>',
    scope: true,
    link: phoneListPostLink
  };

  // Functions - Definitions
  function phoneListPostLink(scope) {
    scope.phones = [
      {id: 1, name: 'Samsung Galaxy', os: 'Android'},
      {id: 2, name: 'Google Nexus', os: 'Android'},
      {id: 3, name: 'Nokia Lumia', os: 'Windows'},
      {id: 4, name: 'Apple iPhone', os: 'iOS'}
    ];
  }
})

So far, so good. You have an almost identical route and directive for tablets and everything works fine.

Soon, your list of available phones and tablets grows and you need to add a filter feature. Piece of cake, you just add the following snippet to your directives' templates:

<div>
  Filter:
  <input type="search" ng-model="search.name" placeholder="Name..." />
  <input type="search" ng-model="search.os" placeholder="OS..." />
</div>
<li ng-repeat="phone in phones | filter:search">

As simple as that, your users are able to search for phones and tablets by name and OS. Business is going great and life is peachy.

Fast-forward a few months and your site has grown, featuring several more sections and product categories. You decide that a "global search" widget would be a great addition for your nav-bar. All you need to do is add the following snippet to your main template:

<div class="search-widget">
  <input type="search" ng-model="query" placeholder="Search the entire site..." />
  <button ng-click="search(query)" ng-disabled="!query">Search</button>
</div>

(And of course implement a $scope.search() method on your main controller...)

The rest is history :P
In no time, sales start going down and you are out of business before you know it.

Here is a simple POC to see this in practice: Demo

tl;dr
Use isolate scopes and profit!