Language school insists I have to go back to Germany to change my status of residence

I’m German, currently in Japan on a whv and I am planning to start studying at a language school later this year (everything is already paid and the COE is in progress). However, my language school insists that I need to apply for the visa back in my home country. I have heard from many sources that this isn’t true and that I can very much change my status of residence in Japan (Germany and a few other counties have this privilege). Now, my language school has claimed that they contacted the local immigration office and they confirmed that a change of status within Japan isn’t possible for me. They also made me fill out a form for the COE where I have to state where \*specifically in my home country\* I’ll apply for the visa. I found that strange so I contacted the immigration office myself, and they said that apparently it depends on the language school but it’s possible. My language school however has never stated that it’s a rule in their school, they just insist it’s not legally possible for me which isn’t true. What should I do? If I have no choice, I’ll go back and apply, but it’s really inconvenient in many different aspects than just financially. Is there really no way I can just do it in Japan just because my language school says so?