Actually mark list accounts as stale while they're being fetched.

components/signin/core/browser/gaia_cookie_manager_service.cc

Index: components/signin/core/browser/gaia_cookie_manager_service.cc
diff --git a/components/signin/core/browser/gaia_cookie_manager_service.cc b/components/signin/core/browser/gaia_cookie_manager_service.cc
index 4b2d4a0b4e2968f7f6849172362bc39343cc45fa..aa428fd7e85f76ae327cd257a7a9561aa74ef883 100644
--- a/components/signin/core/browser/gaia_cookie_manager_service.cc
+++ b/components/signin/core/browser/gaia_cookie_manager_service.cc
@@ -448,6 +448,7 @@ void GaiaCookieManagerService::OnCookieChanged(
     bool removed) {
   DCHECK_EQ(kGaiaCookieName, cookie.Name());
   DCHECK_EQ(GaiaUrls::GetInstance()->google_url().host(), cookie.Domain());
+  list_accounts_stale_ = true;
   // Ignore changes to the cookie while requests are pending.  These changes
   // are caused by the service itself as it adds accounts.  A side effects is
   // that any changes to the gaia cookie outside of this class, while requests
@@ -459,8 +460,6 @@ void GaiaCookieManagerService::OnCookieChanged(
     signin_client_->DelayNetworkCall(
         base::Bind(&GaiaCookieManagerService::StartFetchingListAccounts,
                    base::Unretained(this)));
-  } else {
-    list_accounts_stale_ = true;
   }
 }