Off balance sheet is essentially anything that is not posted in the balance sheet. It needs to be posted somewhere and this is where the income statement is used. A valid point is that the income statement and the balance sheet are connected.
On the other hand, there are examples where for example a company keeps assets off the balance sheet by leasing them. Before the Enron Scandal, the accounting standards were not that strict regarding the finance and the operating leases.
The new standards introduce the “substance over form” definition but the leases is not the only off balance sheet treatment. Other examples include joint ventures and other more complicated items especially in the banking and the financial services sector in general.