In the Peterson trial, perhaps it was procedural and not the same situation. But, if a juror was holding out by refusing to deliberate until their case was heard by the rest of the jury, then that should be within proper bounds and not grounds for a juror to be dismissed.
For instance, that juror might say, "You think there is evidence in this case and want me to vote guilty, okay, let's go over it. All of it. And when we find one concrete piece of evidence that points directly to his guilt, then I will vote for first degree murder as all of you want. Otherwise, I don't want to hear any more about it. I'm not voting for first degree murder. Talk all you want."
Is that the case with the removal of the one juror? And if so, was it right for that juror to be removed?
Yes, I have.
But I've never heard it discussed that they can go out and do their own investigations, have you?
Nor have I ever heard of a judge keeping a juror on the panel who refuses to DELIBERATE, have you?