[Headless] Have public_deps chain reflect inclusion chain

components/printing/browser/BUILD.gn

 # Copyright 2015 The Chromium Authors. All rights reserved.
 # Use of this source code is governed by a BSD-style license that can be
 # found in the LICENSE file.
 
 static_library("browser") {
   sources = [
     "print_manager.cc",
     "print_manager.h",
     "print_manager_utils.cc",
     "print_manager_utils.h",
   ]
 
+  public_deps = [
+    "//content/public/browser",
+  ]
+
   deps = [
     "//base",
     "//components/printing/common",
-    "//content/public/browser",
     "//printing",
   ]
 }