Add item to SharePoint Online Library - strange Access Denied exception

I have created a very simple SharePoint Online App. It has a manifest and a website. There is a simple script on a Default aspx. It is trying to deploy the file to a Library and getting Access Denied exception when saving to "Style Library", but it saves OK to "SiteAssets".

Here is a code of Default.aspx of my website:

$(document).ready(function () {
        var fileContents = "alert('Hello World');";
        var context = SP.ClientContext.get_current();
        var hostContext = new SP.AppContextSite(context, decodeURIComponent(getQueryStringParameter('SPHostUrl')));
        var web = hostContext.get_web();

        context.load(web);

        var createInfo = new SP.FileCreationInformation();
        createInfo.set_content(new SP.Base64EncodedByteArray());        

        for (var i = 0; i < fileContents.length; i++) {
            createInfo.get_content().append(fileContents.charCodeAt(i));
        }
        createInfo.set_overwrite(true);
        createInfo.set_url("test.js");

        // !!!   magic starts here
        // !!!   Style Library doesn't work (Access Denied)
        // !!!   but SiteAssets does
        var targetFolder = "Style Library";
        // var targetFolder = "SiteAssets";

        var files = hostContext.get_web().getFolderByServerRelativeUrl(targetFolder).get_files();
        files.add(createInfo);

        context.executeQueryAsync(function () {
            alert("Saved successfully");
        }, function (_, args) {
            alert("Well, it's SharePoint. Error message: " + args.get_message());
        });
    });

    function getQueryStringParameter(param) {
        var params = document.URL.split('?')[1].split('&');
        var strParams = '';
        for (var i = 0; i < params.length; i = i + 1) {
            var singleParam = params[i].split('=');
            if (singleParam[0] == param) {
                return singleParam[1];
            }
        }
    }

And here is my paranoid AppPermissionRequests section of AppManifest.xml file:

  <AppPermissionRequests>
    <AppPermissionRequest Scope="http://sharepoint/content/sitecollection" Right="FullControl" />
    <AppPermissionRequest Scope="http://sharepoint/content/tenant" Right="FullControl" />
    <AppPermissionRequest Scope="http://sharepoint/content/sitecollection/web/list" Right="FullControl" />
  </AppPermissionRequests>

I have tried SharePoint Hosted model and Autohosted model with a same luck.

So the question is - why the behaviour is different and how can I really set Full Control level of permissions to my App?