Nope, I'm not talking about the MY STORY tour CAROLS. That one was lovely and I believe she sang it well live.
I'm talking about this two performances.
04-09-30 CAROLS AX MUSIC-TV
http://download.yousendit.com/20695408573D4C2D
04-10-08 CAROLS Music Station Special
http://download.yousendit.com/D14A2B933C969C18
Maybe she did move the mic away on purpose, so it won't be too loud. But there are performances, such as the CAROLS she did for Best Artist 2004, where she kept the mic close to her mouth during the same part and she sounded exactly the same. That's why I think that she might have lip-synched those performances. Maybe 'cause her throat was sore?