Anyone can get through with just a state-issued ID and a BC, I just did it the other day, and I'm a few years over 16!
If you hit a border patrol agent who's a new hire they'll give you about a thirty-second speech about how long they've wanted people to get passports, they hand you a brochure and that's about it. If it's someone who's worked there a while, they won't even bother looking at the BC when you try and hand it over, probably just wanting to get the line moving.
Also, does she have a photo ID from her high school or a Social Security card? I think as long as you're showing that you TRIED to bring ID it speeds up the process, but you should be fine. For example, I went on a last-minute trip earlier in the month with someone who is Hispanic, is a US citizen but has a HEAVY Nogales accent, didn't even have her BC with her, the car was in her ex-husband's name and we STILL got through OK after everything checked out.
I wouldn't recommend trying to recreate that last scenario, btw!