Microsoft has different types of partners with many different competencies. Being a Silver Partner does not necessarily mean that you are a Certified Partner for Learning Solutions. In fact, if you don't have any MCTs, then you are most certainly NOT a CPLS.
So, does your employer need to have an MCT in order to teach courses? Only if they are teaching Microsoft Official Learning Products in public courses. This is only allowed to be done by MCTs working for a CPLS. If you are teaching private courses, or if
you are not using MOLP courseware, then it doesn't have to be done by an MCT (but it is a good idea to hire an MCT even if the class is private; MCTs are trained professionals prepared for teaching these courses).