The use of forcing in Set Theory is to investigate the Zermelo-Fraenkel *axioms* and their consequences. This is a perfectly valid use of Model Theory — the Completeness Theorem says that a statement φ is a consequence of ZFC if and only if φ is true in *every* model of ZFC. If one can produce a forcing poset that forces φ to be false, then we know that if ZFC is consistent then φ is not a consequence of ZFC since any suitable model can be extended to a model of ZFC in which φ is false. If another forcing forces φ to be true, then we know that φ is independent of ZFC.

I'm gathering from your question that you're a Platonist (I'm agnostic but I'll play along). This demonstration of independence via forcing says little about the truth of φ in the Platonic Universe. It only says that further information than the axioms of ZFC is needed to determine the truth of φ. However, these investigations over the past half-century have led to some insight on what statements are indeed true in the Platonic Universe. For example, see these [two](http://www.ams.org/notices/200106/fea-woodin.pdf) [articles](http://www.ams.org/notices/200107/fea-woodin.pdf) by Woodin (AMS Notices, 2001) where he discusses the status of the Continuum Hypothesis.