It is wrong if you consider "wavered from that point" to be a unit. It's not that her trust never wavered from some obscure point, but it never wavered afterwards (i.e. after one simple word had put her mind at ease). "From that point on" as a phrase means the same thing as "afterwards". You also get "from here on", "from now on", and the like.
I seems to understand now. I simply got "from that point" incorrectly at first.