so backing someone up means them fighting in the corner, backing someone up is when you crack someone and they take a step back and are shaken by a punch, and its clear to see that both fighters did this. there were times that mosley was shook by cotto's power and vice versa. [YT]http://www.youtube.com/watch?v=9FSsoR4ZMqc[/YT] hatton is number 3 on this vid, up there with golata and bowe as the dirtiest fighters in the business.
You obviously have not seen enough of Mosley, Shane is a come forward skilled pressure fighter, he keeps coming at you with super fast powerful combination's one after another, rarely have we seen him play the 'boxer' role.
hatton beat a shot tszyu by doing everything that was against the rules, he probably knew that if he fought within the rules the chances were that a shot tszyu was going to give him a beating. and if mosley got in the ring with that tszyu it wouldn't have gone 8 rounds. hatton took kostya tszyus punch and gave him a whole load of low blows and elbows in return.
Cotto was fighting off the back foot for most of the fight and look what Mosley did to Margo, repeatedly backed him up against the ropes, out fought, out punched and out muscled him to finish with a highlight reel ko.