I checked with the Institute issuing the Fellowship grant. The information provided by them might help to understand the situation. They claim that according to the German income tax law:
The precondition for tax exemption is that
a) the stipend does not exceed an amount necessary to fulfil the research task or to cover living expenses and training needs and are awarded in accordance with the guidelines issued by the funding source,
b) the recipient is not obliged to provide a specific scientific or artistic achievement or service or to perform a specific employee activity in connection with the grant.
