Hey Marius,
I don’t know if you ever got your answer or not but I think that I have an answer to your problem. I ran into the same issue as well and here is what I have found. Now I use Adobe Premiere CS6 so I don’t know if this works on older versions or not:
After you lay the video on the timeline right click it. With-in the new pop-up window there should be a selection that says: “Scale to Frame Size” Just click that and it will solve your problem!