Since you have a Dutch long-stay visa (MVV means temporary or provisional residence permit and is what is called a long-stay or type D visa in the Schengen regulations), you can visit Germany under the same terms than if you had a Schengen visa. This means among other things that you should only be visiting, should have sufficient financial means, health insurance, cannot work, etc. But you can legally take a course in Germany.
What you definitely cannot do with a Dutch residence permit is move to Germany or stay there more than 90 days in any 180-day period. The last bit is difficult to enforce in practice but if you simply reside in Germany, you would definitely be breaking the law (both the German and Dutch law incidentally as de-registering when you leave is mandatory in the Netherlands). I don't know how your studies are organized but it seems difficult to follow a full-time bachelor's program in those conditions.
In practice, it will also be impossible to register with the municipality and things like opening a bank account are going to be difficult (but you could get by with a Dutch bank account I guess).
So I think your school is misinformed, you might be able to stay illegally and get away with it but it sounds risky (and Germany is known for handing out reentry bans liberally so this could have serious consequences for the rest of your life). You should really insist so that they provide the necessary documentation to get a German residence permit or student visa, that's the only proper way to come to Germany for a full year.