I think it depends on the campus, the chapter, and the PNM/new member.
In 2011, we gave a bid to a new member who was 16. She graduated high school a year and a half early and even entered technically as a sophomore because of her AP credits and some early college classes she took. Parents had to sign certain forms for sure, but she was a very mature young lady. She's been a great member and we have not seen problems. I think she was really looking for a core of lifelong network of friends and some kind of stability in that regard. Her father was in the military and they moved around quite a bit and she never really had a consistent group of friends. she told me once Theta is her family where someone is always "home" to talk to or hang out with.
I did have members contact me out of concern with her age. It could have been an issue should she have not been as mature, but from an alcohol standpoint, the law and rules for her are really no different than they are for members who are 18-20. The law says no drinking or purchasing of alcohol if under the age of 21. Thus, this applies to a 16 year old just as it does older members. Same thing as a fake ID. It's against the law for anyone to have or produce false identification, so the rule/law would apply to her the same as it would anyone else. From a sex standpoint, 16 is the age of consent in the state of Kentucky so if that was something she chose to do, that would have been her own business I guess.
I do think caution and careful thought should way in on a decision with someone who is younger. Not all 16 year olds are mature enough to handle college life. My 16 year old son sure as hell is not and would not be something his father or I would allow him to do. Then again, I'm sure all of us could give countless examples of 18-21 year olds we know that are/were not mature enough to handle college/Greek Life...