If they didn't back him in August why would they back him in January when they have made it clear that they won't be spending big and are trying to cut costs/balance the books from previous transfer windows? They're not going to get the cheque book out everytime the fans start complaining - that's not how to run a business.
If I was FSG I'd be asking why BR is wanting money for strikers. They gave him the funds to buy Yesil and when he had the option in europe to play either yesil, suarez or morgan he chose to play shelvey up front!! It makes no difference that he scored - the point is, we have strikers available and he isn't using them so why is he trying to buy 2 more? We're not man city!
They're youngsters and are not ready, Suarez is great for us, Borini has yet to do much in his short stint before injury but I've yet to reach a verdict on him. We need a striker that is ready now, not relying on youth so much. But I do fail to see FSG investing largely in what we need, as you've said, the just don't seem willing to invest.