No, they didn't have to have a civil ceremony, where did you say you had read that, (not the Lib Dem handout surely)?
In England they probably did. They could have married in Scotland like Princess Anne, but the CofE guidelines on remarriage of divorced people do seem to frown on remarriage to someone who was instrumental in the breakup of the first marriage. Even though a lot is left to the judgement of the particular clergyman, it would look a lot like special treatment for Charles to be able to do something that most Britons wouldn't be able to do, and that wouldn't have helped his popularity in the least.
While Hoey may be an interesting read, I do have to wonder what evidence he gives to back up his statement regarding Rowan Williams likely decision on a question he wasn't asked or Charles' knowledge of Rowan Williams likely thoughts.
Maybe someone who has a copy of the book could tell us if there are footnotes to that effect. I might have a copy somewhere but I'm not sure which pile of books to start looking in.
Once again, it seems to have been missed, you cannot have legislation in regard to everyone except XYZ, that is not legal under British or European legislation.
I thought there was a law (which has apparently been superseded by later legislation) which specifically excluded the royal family from being able to contract a civil marriage. Apparently when the law was drafted nobody gave any thought to the possibility of a royal being an atheist and not wanting to marry in church.