You are correct, pierrotlunaire0. I take my notary duties pretty darn seriously. Birth certificates can not be notarized.
Whoever is signing the document must be in front of me. MUST. I even made my neighbors wait until they were together, and I've lived next to them for 3 years. I would not trust my own mother to have her SO sign a document notarized by me unless they were both right in front of me.
I keep my notary handbook handy and it's one of the things I actually pull out of my case when I'm about to notarize something. I have my journal, my stamp thing, my squishy thing, the gold foil stars (because using the embosser on that looks so totally cool!!!) extra pens and that handbook. I explain to people why they are about to sign the journal. It's to protect them AND me if anything were to happen and they have to prove that the document really was notarized. if there's ever any question about the validity of the document or my stamp/signature, the journal is there to protect everyone. I also tell them if someone were to change the document after I sign, what's in the journal is the correct one, and if the document has different information, guess who's in trouble? NOT ME!!

Notarizing a copy of a public document such as a birth certificate or death certificate only says "this is a copy" and not "this is a CERTIFIED copy." I instruct people to go to the courthouse for that. People that want a copy of these documents require CERTIFIED copies.
Most people are pretty cool about it and happy to sign it. I've only had one person who didn't want to put down his information. I'm not going to deny services for not signing the journal (because in my state it's not required) but he walked away and said he'd go elsewhere. He was polite about it, he just didn't want his personal information in the journal.