It does because Goku actually studied Hit pretty quickly in base form. Vegeta was getting mad. He never thinks straight when he's mad. Vegeta once again got too cocky. Goku still makes mistakes too but when he's onto something he becomes more sharp in battle. He knew Hit was strong from the start. He only got cheated by Frost because he dropped his guard.
As for Goku going first, I would say I agree but thinking through it again, Goku wouldn't rush into things with an enemy he knew was strong. Goku always makes connections with his enemies unlike Vegeta who wanted to fight straight for the purpose of his pride and over confidence in himself.
As for the Frieza part, I believe Goku knew about his weakness before. That's the reason why he didn't wanna tag out. He was studying him during his fight. He most likely remembered his mistake on Namek with the 100% power form.
Goku had always been smart when fighting even as a child. He just has certain times when he shows it which is why fans appreciated this episode of Super. Vegeta was indeed onto something when he blocked Hit's attack but he was rushing through things with too much anger because he couldn't touch him. If he took it easy, he would have caught onto it and probably still been in the match