Well of course you can change the basis reported by the broker, even if the broker is reporting the basis to the IRS. Brokers are not infallible, though in my experience they come pretty darn close.
In the overall, you over reported your 2012 income and will correctly report your gain in 2015 with your adjustment, so you are in a net over reported situation and it's up to you if you want to amend 2012. Unless you are talking about an absolute ton of money I expect the IRS will never question your change. They probably only see a few million changes every tax year.
Tom Young
