I've wondered about this too. I once tried to organize a round-robin tournament, and discovered that all the other players preferred single elimination despite its vulnerability to noise and lack of a meaningful second place. In the ensuing argument, I discovered that they do know about problems like this, but they don't care, for two reasons:

1. They don't care much about accuracy. Tournaments ostensibly rank teams by quality, but they're used mostly as ritual contests: the audience wants to know who won, not who would most likely win.
2. They don't like complexity or novelty. They're suspicious of any design they don't understand, because they're afraid it might be gamed, or might have perverse incentives (e.g. where losing a match helps you win the tournament), and because they want everyone, even the dumb jocks, to understand the rules.

from Wikipedia

In a random knockout tournament (single-elimination without any seeding), awarding the second place to the loser of the final is unjustified: any of the competitors knocked out by the tournament winner might have been the second strongest one, but they never got the chance to play against the losing finalist. In general, it is only fair to use a single-elimination tournament to determine first place. To fairly determine lower places requires some form of round-robin in which each player/team gets the opportunity to face every other player/team.

Well, on the surface level, Team B lost their first match and won their second, while team C won their first match but lost their second, so clearly order matters.

On the more meta level, a format optimised for selecting one winner has been poorly adapted to the task of selecting three winners and ranking them. Adjusting the format to fairly select silver and bronze would add complexity and cost and time, and apparently not enough people care enough about fairly selecting silver and bronze for this to have happened.

[Delted: Didn't think about the question properly]