I'm not a native speaker of Swedish, but if Danes really say "det tror jeg ikke", as just-a-Nugget did, it means in Swedisch "I don't BELIEVE that". "I don't think so" would be "det tycker inte jag", where "tycka" is an expression of opinion rather than trust (as in "believe"). Maybe the missunderstanding is based on that Swedes hear "I don't believe/trust you" rather than "I have a different opinion".
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I'm not a native speaker of Swedish, but if Danes really say "det tror jeg ikke", as just-a-Nugget did, it means in Swedisch "I don't BELIEVE that". "I don't think so" would be "det tycker inte jag", where "tycka" is an expression of opinion rather than trust (as in "believe"). Maybe the missunderstanding is based on that Swedes hear "I don't believe/trust you" rather than "I have a different opinion".