If she wrote what you did, then she might have a point. (My understanding of English really is that an argument can mean debate as well, or maybe confusingly, the debate consists of arguments.) If you're talking about people who have power over another, that's a different situation. But then, that wouldn't exactly fit with majority of "vim vs. emacs" type discussions I have ever had, even online, so the argument (see :-)) breaks down.
In cases where you are arguing with peers, I think people back off in debates in cases where their own argument is not very strong. If I tell someone strong in Java, say, let's do it this way, and he (loudly) says "no way", without explanation, I may think, "OK, this guy knows Java really well, I respect his authority on the matter, then probably my idea is not very good". And I may decide to drop it, not worry about it, and do more useful things. If I think I have a strong argument, I may pursue it and let him explain his reasoning. This is actually not submitting to authority, it's respecting it. If I think he doesn't know Java, I would always pursue. It may be sometimes wrong to do it, but it's also very efficient most of the time, not to have endless debates with people who know what they are doing. That's why it's always a call, and if you want to be really professional, you should not be afraid to pursue a good argument, regardless of what the other party is doing. (And if you work for a boss/authority who doesn't recognize it, I suggest change of job.)
I work for American company, and I can tell you, American act far more "professionally" than Czechs, and sometimes it is indeed really nice. Czechs are also a bit more honest - if they feel something is wrong, they will tell you straight. So trust me, what she describes has not much to do with competitivness.