Hi Deion ,
Thanks for the question! As always in the LSAT world, you can never say never
While your statements are generally true, exceptions do exist and that's why I didn't take it a step further and make it an ironclad relationship. For example, you might read a Fact Set, and then the question stem might supply a statement as the conclusion or hypothesis, and at that point any question type could be used. But, those are exceptions, not the rule, and it is the case that fact sets are normally followed by one of those three types.
Please let me know if this helped. Thanks!