They probably have to gain the support of their Federation (and government?) to receive funding.
Based on reports elsewhere, the guy is a multi-millionaire. They probably need the support of the federation to be allowed to enter, but I think this team funding is not an issue. Since the guy is famous in Turkey, I haven't seen anything that makes it sound like the federation doesn't support the team, even if not monetarily- this is raising so much awareness of the sport for them.
Competing at a high-profile comp would be a stronger showing, making a case for the need for more support/funding.
Nebelhorn is only high-profile in an Olympic year, because it is the qualifier. Basically, Nebelhorn IS the olympics for the teams hoping to qualify (they have no shot of doing well at the actual Olympics, they just want to be there). So why would you go to the 'big one' as your FIRST competition?