data is fair game to be used in your predictive models. There are laws that (varying by jurisdiction) prevent you from leveraging age, gender, race, religion, genetic data, credit scores, zip codes, etc., even though these factors would increase the predictive accuracy of your claims models and help you "optimize" rates.
The concern here is that predictive models like FPI, place some amount of weight (however small) on things that unfairly bias the ratings (e.g. performance from prior seasons, recruiting rankings, implicit conference affiliation, etc.). Fans would feel much better about the rankings if they were certain that the criteria considered only things relating to the on-field performance for that season.
If FPI wants to continue using a Bayesian framework, they need to start using uninformed priors and give every team the same starting point and let the model optimize parameters as the season goes on. Yes, it will be less "predictive" early in the season but it will be much more fair.