All that should matter is weather or not a song sounds good. If it does, who cares if it is recorded beforehand and lip synced. Remember, tons and tons of people and sing and act very well. It's easy. Performers are famous because they can put on a big budget production, not for having the right voice.
Lip syncing is not important. Whether a celebrity such as Anne can do it or not or whether she can sing does not change much in the world. If she has to lip sync or sing in a role in a movie she should do as she must, but she is primarily an actress and should be known for that.
Anne Hathaway is an actress not a singer. The fact that she has chosen to lip sync in a few of her roles shouldn't matter. After all, Audrey Hepburn lip synced in My Fair Lady, and Natalie Wood did in West Side Story. These are actresses, they are hired to play a role, the issue of whether they can sing is secondary. In movies its not uncommon to see some lip sync. Now if someone is making a living as a singer using a voice that doesn't belong to them that is another issue all together.
I am a fan of Anne Hathaway, but I really don't care if she can lip sync. I can lip sync if I really wanted to, but is it something that people care about- No! This is rather stupid. I've never once thought about if a person can lip sync.