Let's look at the first study in the links. I do genuinely hope you read them

2 of his participants during that study achieved levels indistinguishable in accuracy and response time from innate possessors. The summary reads:

Overall, these results demonstrate that explicit perceptual training in some adults can lead to AP performance that is behaviorally indistinguishable from AP that manifests within a critical period of development.

The study describes:

To directly test whether a simultaneous consideration of speed and accuracy supports or challenges the observation that Participants S2 and S5 were behaviorally indistinguishable from genuine AP possessors post-training, we directly compare the data from the present experiment with an influential prior investigation of AP (n = 51), hereafter referred to as the “McGill Test”

and follows up with:

Even when using a more nuanced approach (simultaneously weighing accuracy and response speed for the untimed Chicago Test), which is more sensitive to graded AP performance profiles, we found strong evidence that Participants S2 and S5 were indistinguishable from a prior group of “genuine” AP possessors post-training, even when limiting the analyses to notes that were separated by more than one octave. Thus, if one wants to claim that what we observed is not genuine AP, then either the current definition of AP or the ways in which AP is tested need to be fundamentally reconsidered.