This is true, Sasuke's susanoo is standing because of Naruto Kurama chakra. If you look at the pages well, you will see that when he was making the susanoo, he had the cloak over him but by the time the Susanoo was standing, the cloak was gone.
First of all, what is the cloak? ask yourself again! It is basically chakra. And we saw how other shinobi got even greater depths with their own technique when the chakra was over them... for example: Kakashi, Hinata, Akamaru (the dog) etc...
So now where did the cloak go when Sasuke was bringing the Susanoo? He used it up, the guy is good at manipulating chakra and he had already heard of a standing Susanoo when Hashirama told him about Madara and he has also heard how Madara used Susanoo on Kurama, which is what he is doing successively.
You dont need PROOF!!! it is common sense and ability to use your eyes properly. Just go and read it and watch carefully... unless you need Sharingan to see, in your case it might be better going to spec savers:devil: