It's a simple question, but I think it might help if I add in context. In the paper introducing Functional Decision Theory, it is noted that it is impossible to design an algorithm that can perform well on all decision problems since some of them can be specified to be blatantly unfair, ie. punish every agent that isn't an alphabetical decision theorist.
The question then arises, how do we define which problems are or are not fair? We start by noting that some people consider Newcomb's-like problems to be unfair since your outcome depends on a predictor's prediction, which is rooted in an analysis of your algorithm. So what makes this case any different from only rewarding the alphabetical decision theorist?
The paper answers that the prediction only depends on the decision you end up making and that any other internal details are ignored. So it only cares about your decision and not how you come to it, the problem seems fair. I'm inclined to agree with this reasoning, but a similar line of reasoning doesn't seem to hold with Agent Simulates Predictor. Here the algorithm you use is relevant as the predictor can only predict the agent if it's algorithm is less than a certain level of complexity, otherwise it may make a mistake.
Please note that this question isn't about whether this problem is worth considering; life is often unfair and we have to deal with it the best that we can. The question is about whether the problem is "fair", where I roughly understand "fair" meaning that this is in a certain class of problems that I can't specify at this moment (I suspect it would require its own seperate post) where we should be able to achieve the optimal result in each problem.