I've always thought that if Caroline had been injected with truth serum, the letter would read like this:

"You are a convenient and ever-so-willing guest to prevent us from being bored.If my brother and his friend were here we would have not even thought of you. And by the way, this invite is not at all meant to show our support for a match between you and our brother - if it was, we would have made sure he did not dine out, so don't be getting any ideas.