@roger,
I found the Chinese address for AmericanPress, which exactly mean what you said in your reply to my question.
And the Chinese Name does suggest that it has to do with transportation.
I suppose the American Express was given a wrong Chinese name. Or the translator who did the translation thought that "Express" meant "fast transport" or "fast delivery", or something.
As a matter of fact, many American companies, past or present, have had different Chinese names, carrying knowingly or unknowingly very different meanings. So this is the conclusion I intended to arrive at.