even the BAMF says that an integration course is only a in these cases a must:
"Can immigrants be made to attend an integration course?
Foreigners who received a residence title after 1 January 2005 (new immigrants) must attend an integration course if they cannot make themselves understood in simple or adequate German (depending on their residence title).
Recipients of unemployment benefit II can also be required to attend a course. Other immigrants may also be required to attend a course if they have special integration needs. For example, this may apply if a foreigner is responsible for caring for a minor living in Germany and cannot make her or himself understood in simple German, with the result that he or she has not been able to integrate into German society.
Ethnic German repatriates, German nationals and citizens of the European Union cannot be obliged to attend a course." (Source: http://tinyurl.com/y7my47h5
One of the objectives of an integration course is to learn the German language, so that you can communicate in Germany.
But the final examination of an integration course contains a "Living in Germany" test, that isn't covered by a language course. See detailed informations here: http://tinyurl.com/zvwdljy
So I think the VHS is right. But it would be advisable to pass the "Living in Germany" test to demonstrate that you are well informed about life in Germany.