Burnham wasn't trying to make an argument that Ariam didn't need to be spaced... she just froze and couldn't pull the trigger.
That's not "being wrong". Although honestly it is one of the better Burnham moments, it's "being human".
An arbitrary distinction which serves only to muddy the waters of your flawed argument.
Was she right not to press the button?
No.
Therefore she was wrong.
See?