If you're a mobile mortgage broker as your sig line says, you may have a slight issue with taping customer conversations without their knowledge. I used to work for a bank and lemme tell ya - disclosure disclosure disclosure! Otherwise, that taped call is useless and might get ya into some hot water.
That being said, I have no clue what phone will do that without pressing any buttons. The LG 8100 will tape the call, but you have to "press some buttons" during the call to do it.