The idea is that if Sweden and Finland are not members of NATO, their airspace would be closed to NATO air forces in a NATO–Russia conflict. Then the only way to reach Baltic airspace would be flying past Kaliningrad.
Also, as far as I understand, the combat radius fighter jets is quite short. It's something like 500 to 1200 km, depending on aircraft type and weapons load. Having bases 100 or 200 km closer is already a significant advantage.
Tankers won't help here. The problem is that NATO fighters would effectively have to fly over Russia before they can reach the Baltic states. The area where tankers can operate safely already has plenty of NATO airbases.
