Is it really that complicated? It seems like, at least if you subscribe to a certain definition of fact, it becomes straightforward.
Example Fact: I observed that in a sample of X smokers who smoked Y cigarettes a day, Z developed lung cancer.
Example non-Fact: Smoking causes approximately Z rate of lung cancer.
The fact is about an observation that definitely indisputably happened. The non-fact is an extrapolation which is probably close to accurate given sufficiently good studies, but is nevertheless an extrapolation from facts rather than a fact itself. "Gravity is just a theory" and all that.
By this definition of fact, there are actually relatively few facts of general interest. Most of what we're interested in are theories we derive from facts which is where interpretation comes in. There may have been other confounding factors in the study, but as far as the study results are concerned, those were definitely what was measured.
However, my question is genuine. Is this a simplistic view of what a fact is, and if so, why?