When Sam asks the host if there is a rule against texting one-handed, her hand is clearly not glued to Cat's foot.
Butler said setting a TV to mirror phone will let you see his phone screen on the TV. But when he was texting, the keyboard wasn't shown on the TV, similar to how all the updates on Victorious never show the keyboard. The same happens with the other competitors' phones.
It doesn't make sense to use the same text for every round of the competition, since that way competitors could know what to type before it's their turn.
Everybody kept saying that Sam hand is glued onto Cat's foot but it was actually glued to her ankle.