That said, the Doctor might be 100% right to be wary of her. He has no idea whether she is friend or foe - and to be honest, neither do we. When Martha (finally) stood up for herself, we knew that she was justified. Whereas we've no idea who/what Clara is and if she was just trying to put him on the back foot - which is what happened
The only mistake was him warning her that he was suspicious of her. He should have handled it the way he did with Amy - be discreet until he understands what's going on - until he realises just how she is possible. If it transpires that she's a plastic replica of 'Clara', and the one who sticks a knife between his shoulder blades at Trenzalore, that'll learn him!