You have confused me by staying quiet about it or you have got me confused by staying quiet about it?
I know the latter is correct, but is the former sentence correct as well and convey the same thing?
Your preferred (second) sentence uses the word confused to refer to an attribute or characteristic of a person I am confused.
The same word can be used to describe (in the past tense) the action of another person to produce that attribute You confused me.
So the two statements do convey the same meaning.
Life becomes a little more complicated when the state of befuddlement arises not from the actions of an external agent but from one's own.
Because I removed he flange before I disconnected the lubricator, I confused myself when it came time to adjust the reciprocator is a more honest expression than The instructions were very confusing.