It implies none of those things. New Amsterdam was founded in 1624. New Amsterdam became NYC. The sentence is a typical structure making an joke which basically

It implies none of those things. New Amsterdam was founded in 1624. New Amsterdam became NYC. The sentence is a typical structure making an joke which basically says crime existed in NYC from the start. You are somehow missing the context both of that threadbare joke, and the context of the paragraph it is in, and the article as a whole, leading you to ascribe implications that aren’t in any way present in the writing.