Is this true, can a BG simply leave by stating he is doing so?
Yep. You can use deadly force to stop an imminent attack, but if the perpetrator says he's leaving, let him go.
If you use any degree of force to restrain him when he's not actively threatening you, the matter could quickly escalate to use of deadly force. Then things will get problematic when it goes before a grand jury. If you harm him in any way, there could also be repercussions in civil court.
New Mexico doesn't have an actual castle doctrine. They have an old law dating back to 1907 that precludes a duty to retreat, but caselaw is sparse and unclear.