Being cautious and being scared often have the same result. One is credible and one is not. The two flip-flop (and excuse each other), but that time I call it scared.
According to the show, a 24 hour refueling stop by the reinforcement group, allowed the Japanese (second force) to arrive first.
Why would under fueled ships set sail for a rescue mission? Did they think they wouldn't need fuel?
Why would you stop for 24 hrs to refuel at sea? Is that easier than refueling before they started? Did they leave with the tanker or rendezvous on the way?
Who gave these commands?
Why turn around when you are 5 hours away, when you could've been 19 hrs early?
Are their tanks so small that they needed to be topped off to get to Wake? Didn't the South Dakota sail from Guadalcanal to New York without refueling?
It appears he (Pye) was looking for an excuse not to do it, because I believe he would've been out of his element when he arrived, and things would've gotten worse in a hurry. He (Pye) was (with a viable excuse) avoiding something he couldn't handle. Which is why (I dare say) he was replaced.
I compare Pye to LLoyd Fredendall....too little, too late.
just an opinion.

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Morbius, Morbius! Something is approaching from the Southwest. It is now quite close.