The wide adoption of virtual learning environments such as Moodle in numerous universities illustrate the growing trend of e-learning development and diffusion. These e-learning environments alter the relationship between the students and academic knowledge and learning processes considerably stimulating the students' autonomy by making most of the course material freely available at any time while inducing a progressive reduction of physical student-teacher interactions with virtual ones. Recent advances, as proposed in the TeSLA project, even introduces an e-assessment environment. This entire virtual learning framework raises new concerns in terms of privacy, given that such environments are potentially able to track the students, profile their habits, and retrieve personal data. In this paper, we analyze the influence of conception paradigms of e-learning platforms on personal data protection, based on a classification of these platforms in two antagonistic approaches. We illustrate our analysis with a case study of the TeSLA project and examine how the design choices impact the efficiency and legal compliance of personal data protection means. We finally propose alternative designs that could lead to significant improvements in this matter.