Because the wording of the Italian lends itself to the more accurate English past tense, although the translation still avoids English subjunctive. Most of the time, Duo is using extreme "artistic license" when translating the past-tense subjunctive imperfect into indicative present.
Perhaps that is because the more literal translation into English past subjunctive is too stuffy or non-colloquial (not everyday) for Duo's taste. Instead of trying to translate Italian past-tense subjunctive into English past-tense subjective, Duo uses present tense English indicative or past indicative progressive (as here) because that is the only way Duo can make it work to Duo's satisfaction.
If this sentence were actually translated into subjunctive, if would be: "I believe she were using me." There's a nuance to that phrasing which is missing from "was using".
"were using" signifies that the use/misuse is uncertain - the speaker doesn't know, nor can anyone else know, that she may have been using him. With "was using", the use/misuse is not uncertain, it is 100% certain. The only thing that's uncertain is what's in the mind of the speaker.
More clarification here requires more context, which is not present. The point, however, is that there is a very real difference in the two English translations, and the abandonment of English subjunctive disserves us all by eliminating one of those forms of statement.
The “tips and notes” of the Subjective Perfect section states the following:
“Occasionally you will see the imperfect subjunctive following a present tense verb to show an action occurring before the main verb”.
In this exercise: “I believe (now) that she was using me (in the past).”
I think the alternative correct solution DL offers is incorrect: "I believe that she was using me" is in fact the translation for " credo che lei mi stesse usando". Which is different from "credo che lei mi usasse", and different meanings. Although both sentences refer to the past, there's a continuity of action in the first. I reported it of course; just wanted serious learners to know.