The jī of wēijī, in fact, means something like "incipient moment; crucial point (when something begins or changes)." Thus, a wēijī is indeed a genuine crisis, a dangerous moment, a time when things start to go awry. A wēijī indicates a perilous situation when one should be especially wary. It is not a juncture when one goes looking for advantages and benefits.The word for opportunity, is actually jīhuì. Huh.
Aside from the notion of "incipient moment" or "crucial point" discussed above, the graph for jī by itself indicates "quick-witted(ness); resourceful(ness)" and "machine; device."
Let's hope no one's been taking unnecessary risks based on the justification that the Chinese language told them to. I'm talking to you, JFK, Al Gore, and Condoleezza Rice.
Even if it were true that jī meant opportunity, I've got to categorize this as some variation on the equivocation fallacy or etymological fallacy. The equivocation fallacy is when you switch around different definitions of a single word. The etymological fallacy is when you assume that a word or expression's historical meaning must be similar to its current meaning.
Just because some particular language gives a word two definitions doesn't mean that those definitions are the same. Similarly, the fact that some particular language joins two words to make a new one doesn't necessarily signify anything. Someone at Language Log compared such reasoning to trying to analyze "butterfly" in terms of its constituent parts, "butter" and "fly". Next, try "hangover" or "checkmate", see if that gets you anywhere.