That is not what I meant. Both are objectively measurable results - of course if you look at critic voices the details in their implementation differ, but in general yes.
But there are different ways of implementing something and which one you choose depends on assumptions. If you use Field Equations for describing relativity you need a certain set of assumptions. If you use a different mechanism to describe relativity, you need another set.
You can't build a theory without assumptions.
Eh.. no? That's literally the opposite of how it works: it's not two strange assumptions causing all this weirdness, it's two very strange observed phenomena for which these two models give the best predictions, so far.