If we are talking about an initial interaction between two strangers, then clearly looks are important. I think anyone who believes otherwise is deluded.
Look (no pun intended), when we see someone for the first time, it's human nature to form an initial judgment (a first impression) based purely on how they look/ act. That will determine whether or not the recipient will give them the time of day. Their personality won't even get a chance until / unless they've made it past that first hurdle. IMHO, the only viable ways the personality can really come through despite adverse looks are if a) they are part of a larger group of friends or b) they're in an environment like work or some other project where they're forced to interact with each-other. However, I would like to say that I'm not, I repeat NOT stating that you need to be a 6' Chad with guns, abs and a 'douchebag' haircut to get a girl... you just need to have the right sort of look that the particular girl goes for (Oh, and it helps if you make an effort to look presentable). As has been said multiple times on this board, looks are subjective.
The OP doesn't mention the show, so I can't comment on the specifics of this incident in question; HOWEVER... it's all well and good saying he's "nice", but what does that mean exactly? This is just my opinion, but being "nice" isn't the same as being charming, witty, charismatic, self-confident or funny (N.B. these are specific qualities that girls are known to like). Alter boys and boy scouts are nice guys, are you telling me that automatically entitles them to a free sex pass with every girl they walk past?
General rule of thumb, men are visually stimulated, women are emotionally stimulated; i.e. guys like women who look good (that's why it can be easy for an average woman to get a lot of male attention if she wears tight or revealing clothing)... girls like guys who can make them feel good about themselves (why girls say they like guys who can make them laugh, feel important / special)... it just so happens that for some "feeling good" means having a dashing "stud-muffin" on her arm (WTF does that even mean LMAO).
As for the argument itself, I think it was a pretty stupid thing to say to her, and the OP kinda asked for that put-down (if you don't mind me saying). Granted, there may be an element of truth in his argument, but there are some "trigger" things you just don't say to women... it's almost on a parr with saying that she's fat (even if she is/ was), or that you fancy a threesome with her bestie. She was wrong to bring her ex into this, but he did push her into a corner and he also described a completely hypothetical situation... I mean, apart from suckers on scamming PUA courses, who really goes up to random women in the streets and just asks for their number without even trying to chat them up first?
IMHO, both parties should apologies, but the OP should make the first apology, for creating the stupid situation in the first place... it was a completely pointless argument.