If the earth is the subject, and there is only one earth, is controlled study weakened?

Wow, good question. First I would say that we need to take the predictive models on a case by case basis. The level of reliability for each greatly varies. A very important concept in science is known as consilience or convergence of evidence. In our context, this is the idea that multiple models will point to a demonstrable conclusion, even though some valid models will not. This is why deniers (of any scientific fact established from theory) cling to the outliers that confirm their position and ignore consilience.

This might be best explained by thinking of a study of coin flips. Let's say that 20 studies were conducted, 19 of which found no statistical difference between heads or tails (what we call having a p-value greater than .05), and one study, out of pure statistical probability, found that heads came up more a statistically significant number of times (p < .05). We can look at this the following ways: 1) focus on the one statistically significant study and claim that coins unfairly land on heads, which is clearly fallacious. 2) Reject the methodology (models) because one came up with completely different results, which is a poor conclusion, but more due to a lack of scientific understanding than fallacious reasoning. Or 3) accept the convergence of evidence pointing to the fact that coin toss results are functionally random*, which is by far the best conclusion based on the scientific method and reason.

* I say functionally because one can get into deep philosophical debates about randomness, which is irrelevant for this example. Also, there are studies that suggest that more than randomness might be at play.