A mullet is a hairstyle which is short in front and long at the back, and is often connected with "rednecks".
So it looks as if this unwritten rule is that because a boxer with this sort of hairstyle is likely to be tough, he can take more punishment. Alternatively it could indicate that referees don't like men who have this hairstyle so allow them to take more punishment.
A mullet is also a type of men's hairstyle that has short hair on top and longer hair at the back. Most boxers I've ever seen have either the shortest hair possible or they shave their heads, so obviously there is a metaphor here, but I'm lost as to what!
I tried googling mullet and boxing, but didn't have luck.
Did you try the Urban Dictionary? I can't access it here but it may shed some light on this obvious slang usage.
Edit: Oh, while I was trying to further research, I ended missing being the first to respond, and I didn't want you to think I was contradicting Anglika.
"Sportin'" is slang for "sporting," which in this case means "wearing."
As Anglika and Barb mentioned, a mullet is a hairstyle that, when viewed from the front, looks short and conservative, but in the back the hair is long and cascades to the shoulders. (It is often described as a "business in the front, party in the back" look.) I believe the quote you mentioned is referring to this "viral video" that has been circulating on the Internet.
Actually that "quote" was referring to Tommy Morrison who was much better boxer than this one hi hi.
However he once suffered a very brutal knockout by Ray Mercer who managed to punch Tommy 4 or 5 times after he had already lost his consciousness.
Tommy Morrison had this special kind of hairdo that you can probably call a mullet. YouTube - Tommy Morrison VS Merciless Ray Mercer