I'm not entirely sure of the guidelines, but it could also be because the pathogen causing the influenza is found in the bloodstream during an infection? I don't think a runny nose should be of any concern though.
According to this article:Influenza A virus is easily transmitted by respiratory aerosols and droplets and has high epidemic and pandemic potential (1). Influenza viremia may be established within 2–3 days before onset of clinical symptoms (2), implying that this virus is hypothetically transmissible by blood transfusion. However, transmission has never been confirmed, and efforts to detect influenza virus RNA among blood donors have been unsuccessful
That being said, if the flu virus has never been detected in the blood, why should they deny a donator? I suppose they are just practicing the 'better safe than sorry' approach, and don't want to potentially taint the good blood with bad stuff.
Best to just wait till you show no symptoms, including the runny nose. Everyone is so sensitive these days