Both of your reasons are true:
Option 1 happens:
Evidence is definitely language-dependent. If I want to do statistical analysis on the genome of rabbits, I need to know what is and what is not a rabbit, so I can go to my taxonomy and get the definition of a rabbit, and then go find some. Twenty years ago I could also do that for dinosaurs, and find that they were all extinct. But now, if I do the same, I find that birds fit the definition given for dinosaurs.
So whether or not all dinosaurs are extinct depends upon a definition that is subject to change. This is not the way we ordinarily think of science working, but it is not so exceptional.
For a worse case, consider the definitions of mental disorders, these have been rewritten five times since the 30's. If I am running experiments on psychiatric drugs, that means that there are people who might not have met the diagnosis in DSM IV, but will in DSM VI. Whether or not my drug 'works', in the sense of reducing the symptoms of a given described disease, might depend on when I tested it.
Theory moves around not just facts, and statistics, but definitions, as it evolves.
Option 2 also happens.
From a Kuhnian point of view, a group of definitions, statistics, and laws holds together into an organized whole, that he calls a paradigm. Paradigms shift, when the paradigm starts failing to cover known data, or begins to have odd limitations on its explanations.
The transition from Newtonian to Relativistic notions of space in Astronomy is such a paradigm shift. Newtonian physics did not accommodate our measures of light's speed. So various things had to be shifted to accommodate this. This happened pretty cleanly, but other such transitions were not as quick.
A slower example is the atomic theory of matter. Various alternative explanations fought it out for consideration, and each way of covering the facts turned out to be inconsistent with other accepted parts of the paradigm they were trying to expand. These dead theories are sometimes recounted in courses on the subject. Boltzmann, for instance, was so disparaged for promoting atoms as an alternative that he was forced out of physics and into philosophy. Ernst Mach, otherwise known as being as brilliant in physics as philosophy, is famous for holding out to the bitter end in his opposition to these theories.
People who were advocates for the paradigms that eventually failed to explain heat and other effects without atoms, did exactly what you indicate. They kept doing what they thought was justified, and the overall paradigm shift was not complete until they were hegemonized out, backed into irrelevance by the incoming data, and the way it affected opinion and understanding.
To a lesser degree, every science always has smaller versions of this kind of paradigm shift going on. For instance genetics has a gap between continuity in evolution that makes statistical tracking of mutations a way of measuring past populations, and the notion of punctuated equilibrium: that change, especially extinction, tends to happen suddenly, so that measuring this kind of thing over time, presuming it has some kind of smooth rate of accumulation, is misleading -- big die-offs are going to skew your distributions too much. This is an ongoing tiny little paradigm dispute.
(An example of where they conflict: By the continuous standard you can estimate seventeen women from the neolithic era reproduced for every man, from a more 'punctuated' point of view, it is more likely three, with mass eradications of whole nations of men at regular intervals that left the corresponding women with heirs. This is the downside of patrilineality...)
And people on either side are just going on doing what they think is right. Eventually some new data will make one or the other position better, but how much better it has to look, before you buy in, depends on who you are, and how you are positioned in the 'politics' of this issue.
