I haven't done much research on Krav Maga, or actually seen a KM training session... so yeah, grain of salt time... but I'm relatively positive that Krav Maga does NOT teach how you to fight a pro boxer, or an mma fighter, or a grappler.
Krav Maga trains you how to fight against street thugs, how to deal with people who may be armed, how to react when a person comes at you swinging wild. So while a guy who teachers KM couldn't handle a boxer or a grappler, he would deal with your average street thug better than a boxer or a grappler.
The idea is, 99% of the time, the guy who attacks you on the street is crazy or desperate. But mostly untrained.
Now, the idea of whether someone can truly be taught to act appropriately in a street scenario by repeated actions and pseudo-realistic sparring is debatable. But saying "A KM GUY WOULD BE OBLITERATED BY A BOXER" is absolutely besides the point. Someone should go into boxing if he wants to learn to beat a boxer.
Have you seen the training sessions? The training obviously doesn't prepare you to face a real life situation, simply because there is hardly any resistance from your sparring partners. They let you perform these krav maga tactics on them. In a real street fight, there will be wild, fast punches from every direction and stumbling around and the krav maga guy simply won't have the experience to fight a real opponent who IS resisting and IS actually trying to knock the shit out of you. They aren't ready for a full contact match up.
In addition, if a boxer can obliterate a krav maga guy, then technically he would easily obliterate the street thug, correct? Therefore, boxing is a much better form of self defense for a street scenario.
Furthermore, I think the people that train in krav are just lazy and don't wan to train in a real sport. Because lets face it, boxing/bjj training isn't easy. S&C, endurance, etc. are vital in these sports and aren't easy things to accomplish. Also, in a competitive sports like boxing or bjj, you have to face other
trained opponents which will be difficult and you risk getting hurt.
But in krav, you don't have to do all that hard training because the entire time you tell yourself, "oh well the people i'll be fighting won't be trained anyways, so i'll easily take them on". Krav maga is great because your training partner isn't resisting and they easily let you perform all these submissions. Makes you feel powerful.
This video says it all.
Keep a look out for 00:15 seconds in, where he hits the guy with a rolled up magazine. Shit is deadly for sure.
The point is, what is shown in this video isn't realistic. Much like aikido. Not full contact.