Is there suppose to be commas around she said or is it grammatically correct to have no commas in this sentence?

After Caroline began the meeting she said "I am going to dinner."
Ooh goody - a grammatical gray area.
People disagree about this one.

I believe that TECHNICALLY, since "I am going to dinner" is a clause, it follows that the clause should be separated from the rest of the text, and so TECHNICALLY, a comma is required.

I think that in the somewhat similar sentence:

She said "hello"

You DON'T need a comma because "hello" is not a clause and therefore there's no need to set it apart. I could be wrong about all of this, because punctuation has rules of its own, over and beyond grammar - rules that change, moreover, as you cross the Atlantic. However, in a sentence such as:

She said, "I am going to dinner"

many authors feel that the comma is unnecessary, and don't bother with it. Personally, I don't feel that the comma there is intrinsically 'right', and I tend to substitute it with a colon - but this is a personal affectation which hasn't really caught on outside of me.

I hope other people with differing opinions join in on this thread...

I think that you're right to say that the comma's not necessary, but I don't think I'd put a colon in either, unless you're aware that it's an affectation and you're not trying to be grammatically correct or anything! Where you might use a colon is in something like a newspaper article:
The victim, speaking from her hospital bed, said: "That's the third time it's happened this week."

In other words, reported speech versus narrative (if that makes sense).