Online education and in particular Massive Open Online Courses (MOOCs) are often regarded as a way to solve global educational challenges. In this article, we highlight the students' uptake of such a 'digital solution'. Presenting initial findings from a research project in Germany, we situate our investigation in the specific context of digital educational offers for refugees, using Kiron Open Higher Education as an example. Kiron has designed an innovative academic model, with MOOCs at its core, to ease refugees' access into higher education. Drawing from student data of 1375 Kiron students we look at students' actual usage of the offer and the accompanying support services as well as the difficulties refugee students face while navigating online higher education. Results show, amongst others, rather low completion rates in the online courses and point to a much more nuanced picture of how students make use of the offer -- putting online education as an easy, straightforward formula to the integration of disadvantaged students into question.