Exactly.
Take a pure boxer who's only combative sports experience has been boxing and nothing but. This doesn't mean that the only tools he has access to are boxing tools. There's nothing stopping him from grabbing an opponent, kicking and opponent, choking an oppenent etc. he's not going to go "gee, I could kick this guy in the leg right now, but I better not because I'm a boxer."
not to mention that a big number of boxing's greats (especially in previous eras) were indeed "street people" prior to their boxing careers, and have been in scraps for a good portion of their lives. naseem hamed, despite all of his boxing talent, had (supposedly) gotten his ass handed to him on several occasions in pub brawls. the exact opposite can be said for roberto duran, who was a beast in the alleyways and streets of panama. sonny liston, imo, would've murdered ali had they fought anywhere else besides a boxing ring. street fighting is something you either can or can't do, and the guys who are good are usually the ones who have been at it habitually as they've grown up, and developed that heightened sense of, iunno, asswhippin?...whether it be knowing when and how to hit first, or even more importantly, knowing when the fuck they are about to be set up for a beating, the sport that they pick up (whether it be boxing, wresting, mma, mantis style, gymkata, turbo jam, whatever) can only fine-tune their natural talent for kicking ass.
don't believe me? look at a fella by the name randall "tex" cobb. one of the toughest known guys to walk this earth. bar brawling, karate, kickboxing, boxing, he's been through everything. when he layed out earnie shavers did that mean "karate > boxing lol omg omg"?! no, it meant that randall cobb is a tough bastard whether you're coming at him with a 10oz boxing glove, a shin guard, or a fuckin' pool stick.