Yet it was the answer Sony gave when asked about BC back when the PS4 launched
"No," Yoshida said, when asked about any current-gen PSN game being natively supported on the PS4. "Unless, somehow, some games work on emulation. The easiest thing technically would be to make PS1 games work on PS4 through emulation. But we aren't talking about our emulation plans as yet. There are two ways: emulation or cloud service. But native support, no, sorry. We could do so if we choose to. We know who purchased what as a record. But we are working on service plans, and we haven't decided."
http://www.engadget.com/2013/02/21/psn-transfers-ps4/