No, the numbers are definitely not wrong, but when he says he "reads statistics" it means he just "looks at the numbers and regurgitates them into a camera." He doesn't actually read and evaluate them.
What's happened in Sweden is that we have a much lower bar in the country of what constitutes rape and sexual assault. While in many countries rape might be only when there is penetration, rape here can mean touching of the genitals of a non-consenting person. We take this very seriously. Hopefully just that will make you realize that the number of reported incidents from that alone will make the numbers soar, and you would be right.
We also have a policy in Sweden to actively encourage victims of rape and sexual assault to come forward and report when it happens. They are heavily protected by law which lowers their fears of repercussions when reporting it.
This also increases further the number of reports. Think of it as sort of the same situation with what happened with autism, the definition of what autism is got broader over time, and with a broader definition you get more reported cases of autism, not an actual increase of actual autism as compared to before.
So, the problem is that when you compare statistics between countries like this, you compare number of reported cases to each of their governments, cases that have different standards and metrics in different countries. It is not possible to really do the comparison by just saying "The numbers here are way higher" unless you try to do a complete in-depth review of each country based on the same criteria.