You can't train above your ventilatory threshold while nose breathing, and boxers are definitely training above that level of intensity, at least for short burts. Fighting is anaerobic.
Why? What about this? http://www.journals.aiac.org.au/index.php/IJKSS/article/view...
Conclusion: This study supports the ability of recreational runners to utilize a nasally restricted breathing pattern at all levels of running intensity without loss in VO2max or GXT TE, and with superior PE and VE/VO2, following an extended training period using this practice.