Re: "assumptions don't turn out to be what humans look like when you hit them"
"You can get sanctioned and your UC reduced at the whim of job centre staff and you can do nothing about it"
You can always appeal (AKA "mandatory reconsideration"). (See here: "If you disagree with a sanction decision, or have more evidence, you can ask for a review. This is known as a mandatory reconsideration." There is a link on what to do.)
Please, do not let the fuckers get away with it. Make them justify their decision. It will also make them think twice before sanctioning you again: they know you will be a lot of work.