This is easier to understand if you think of how this would be expressed in the present tense.
In Present-day English the present continuous is often preferred to the simple present in speaking of unique, individual actions because the simple construction is felt to imply repeated, habitual practise. Thus, if the girl were speaking of the gift as it was occurring, she would not say:
Danny gives me this because it is so special.
although that is entirely acceptable, and three or four generations ago might even have been the most natural way of saying it. Instead, she would say
Danny is giving me this because it is so special.
In your example, she uses the continuous form because she is recalling what she thought at the time; in effect she is 'quoting' herself. The past continuous is a 'backshifted' present continuous. It is only when she realizes her mistake after the fact that she shifts to the simple past, which as you say expresses a completed action.