I thnik it is an urban legend that the lack of slots in DUS has anything to do with the lack of intercontinental flights at DUS. There is always a limited slot availability for intercontinental flights as these tend to be operated at off-peak hours (DUS is not a hub airport), by new entrants (which are given priority when slots are allocated pursuant to EU regulation 95/93) or airlines which already hold slots for other services. Anyway, flights to North America depart at noon-time, flights to Asia in the afternoon or evening. No problem to get slots for a couple of weekly flights.
The slot problem has made it difficult in the past for airlines to establish a large operation with aircraft based at the airport because of the overall availability of slots (cap) and the availability of slots during certain hours of the day which are necessary to justify a base.