Having researched further, I agree that rbmartin is correct and I'm wrong. If you look at the fares map accessible here you can see that the journey via Canada Water is shown in green and TfL fares apply whereas if you go via London Bridge the bit of the journey between NXG and LB is red so the combined TfL National Rail fares apply.

Can you buy the £4 ticket at Honor Oak Park / Forest Hill, and, if so, are you prevented from getting out of the barriers at London Bridge - or onto the Tube? Confusing isn't it? But I can't really imagine why anyone living in London would want to buy a cash ticket when it is so much cheaper and convenient to use Oyster.