Being a non-native speaker of English I would absolutely understand the meaning. It is just that the very same sentence constructions are common in German (my mother tongue). Therefore, I would like to say that it is not absolutely wrong to use these expressions interchangeably.
Well, perhaps there is a slight difference between these expressions anyway.
I just saw her once. (Here it is not said when you saw her – you only say that you saw her anytime in the past but not again since then)
I only saw her that one time. (Here you mention that you saw her only one time. It implies (in my opinion) that you have mentioned before what “that one time” exactly means).
I am eager to learn what more advanced English students or native speakers think about your question.