ng-repeat作用域的奇怪行为

我有这段HTML:

<div ng-switch="view">
    <div ng-switch-when="products">
        <input class="form-control" placeholder="Search" ng-model="searchText" />
        <ul ng-show="products && products.length > 0">
            <li class="head">
                <div class="column col-select"><input type="checkbox" ng-model="$parent.allSelected" ng-change="$parent.selectAll($parent.allSelected)" /></div>
                <div class="column col-name">Name</div>
                <div class="column col-code">Code</div>
                <div class="column col-stock">Stock</div>
                <div class="column col-code">Price</div>
                <div class="column col-buttons"></div>
            </li>
            <li ng-repeat="p in ($parent.shownProducts = (products | filter: searchText))">
                <div class="column col-select"><input type="checkbox" ng-model="p.selected" ng-change="select(p.selected)" /></div>
                <div class="column col-name">{{ p.name }}</div>
                <div class="column col-code">{{ p.code }}</div>
                <div class="column col-stock">{{ p.stock }}</div>
                <div class="column col-code">{{ p.price | currency: '$' : 2 }}</div>
                <div class="column col-buttons">
                    <button class="btn btn-edit" ng-click="goTo('edit', $index)"><i class="fa fa-pencil"></i></button>
                    <button class="btn btn-delete" ng-click="goTo('delete', $index)"><i class="fa fa-trash"></i></button>
                </div>
            </li>
        </ul>
    </div>
</div>

$scope.products = [{ name: 'Test1' }, { name: 'Test2' }];
$scope.select = function (value) {
    if (!value) {
        $scope.allSelected = value;
        return;
    }
    var selCount = 0;
    for (var i in $scope.shownProducts) {
        if ($scope.shownProducts[i].selected) selCount++;
    }
    if (selCount == $scope.shownProducts.length) $scope.allSelected = true;
};
$scope.selectAll = function (value) {
    for (var i in $scope.shownProducts) {
        $scope.shownProducts[i].selected = value;
    }
};

这段代码可以工作但是:

• Header (li.head)必须使用$parent scope来访问$scope服务否则，虽然设置了初始值，但模型不会更新正确。
• Ng-repeat作用域不使用$parent，但它工作得很好

在我看来不一致。我知道ng-repeat创建了一个子作用域，但为什么不需要$parent呢?为什么需要$parent，虽然它在ng-repeat定义之外?

更新:

我发布的代码是ng-switch的一部分，所以我也把它放了进去。shownProducts是一个数组，其中包含通过搜索文本过滤的项目。我将该控件添加到HTML中。我还将产品数组添加到$scope.