Collaborative filtering (CF) is a widely-used technique for generating personalized recommendations. CF systems are typically based on a central storage of user profiles, i.e., the ratings given by users to items. Such centralized storage introduces potential privacy breach, since all the user profiles may be accessible by untrusted parties when breaking the access control of the centralized system. Hence, recent studies have focused on enhancing the privacy of CF users by distributing their user profiles across multiple repositories and obfuscating the user profiles to partially hide the actual user ratings. This work combines these two techniques and investigates the unavoidable side effect of data obfuscation: the reduction of the accuracy of the generated CF predictions. The evaluation, which was conducted using three different datasets, shows that considerable parts of the user profiles can be modified without observing a substantial decrease of the CF prediction accuracy. The evaluation also indicates what parts of the user profiles are required for generating accurate CF predictions. In addition, we conducted an exploratory user study that reveals positive attitude of users towards the data obfuscation.