The focus is on the subtle impact of using some framework for analysis rather than the gross impact of individual bias (obviously that's an issue every scientist should be and probably is aware of).

For example, statistical causal models are widely used in the social sciences. After searching within the field, I looked for a problem associated with explanation ambiguity due to how the models were framed (or could be equivalently framed leading to alternate explanations) and found this paper:

MacCallum, R. C., Wegener, D. T., Uchino, B. N., & Fabrigar, L. R. (1993). The problem of equivalent models in applications of covariance structure analysis. Psychological Bulletin, 114(1), 185-199. doi:10.1037/0033-2909.114.1.185

I'm not sure if they could extend their approach using manifold theory and an equivalence class for the set of models, but I wouldn't be surprised if someone did something similar. It could then be an example of a coordinate-free approach to data analysis in psychology.