What you are trying to do is that you are trying to send a tweet using accounts framework only. You haven't written code to send tweet using normal twitter API.
do one thing validate first if you can send tweet using accounts framework. if not then proceed to normal OAuth authentication
you can validate twitter account using
if ([TWTweetComposeViewController canSendTweet])
{
TWTweetComposeViewController *tweetSheet =
[[TWTweetComposeViewController alloc] init];
[tweetSheet setInitialText:@"Initial Tweet Text!"];
[self presentModalViewController:tweetSheet animated:YES];
}
if this condition fails then post sweet using OAuth API. The simplest possible way is to use this control