The ending was staged (spoilers obviously)
Why would the mom ONLY hire a private investigator? The cops would certainly have been involved and there would be more than just these casual questionings from a P.I. There would be several suspects and they would be taken in for questioning. The cell number would have been found out and the car would be found as well. This should be enough of a clue to figure out that she was not missing, but that it was staged and that the the mother writing is actually her.
Nothing can really be believed in the film. We as viewers are supposed to be someone who is reading her blog so we have no idea what is true, since it's anonymous and people are exaggerating and making things up all the time on them. The ending where the real name was revealed is probably not real. Maybe the fact that the professor was a video store clerk is real and that she didn't actually have an affair with the father she was nannying. Maybe.
As she said in the end before she dives in the bath water, she needed a way to end her "reality show" so she makes up the ending for dramatic effect just as she made up the college professor and the affair with Christian Slater. There was really not that much of a reason for someone to abduct her.....I mean there could have been with all the supposed affairs she had (but who knows if those are real or not). The more likely interpretation is that she felt like everyone and the world was out to get her. And she had this blog where so many people say violent things to her. So she wanted to end the blog to avoid all the negativity it created (just like she says to her mother, "why are you soooo negative!!!") and maybe get back at them and have an effect on all the readers who were saying nasty things.
So far all those that are like "who did it" ask yourself why would a P.I. only be hired and not the cops and you have your answer right there.