Um, maybe that he'll make sure her death was not in vain or something regarding punishing or prosecuting the one that did this to her. You don't know when that promise was made. It could have been the first night she was missing. Casey could even be aware of the promise and that statement could have been a big FU to Casey.
I wish people would ease off judging them. He's probably not saying her name so he doesn't break down and so that he can get through his eulogy. Please try to put the pitchforks down for a second and allow him to grieve. At least give him the benefit of the doubt at her freaking memorial service. This is not a vast conspiracy with double meaning in everything. Presume for a moment if you can find it in your hearts, that what he said was as pure as the love he spoke of for Caylee.