In this case its reasonable to suggest that by submitting his altered contract without drawing the banks attention (e.g. by putting at the front "here are my proposed terms") then not only does the bank not have to abide by them, but he was guilty of deception by trying to trick the bank into signing up to them.
Normally these rules are used to protect consumers from fine print proffered by suppliers. For instance https://en.wikipedia.org/wiki/Interfoto_Picture_Library_Ltd_... established that unusual or onerous terms cannot be hidden in a page of fine print and still be enforceable. But the rules apply the other way around too.