See
https://en.wikipedia.org/wiki/Threshold_of_originality#Pre-p...TLDR it's untested in United States court, but yes, the same principles apply. You very well might not own the copyright on that street-corner photo.
There is no way of getting around the human authorship and creativity requirement. There's no loophole that AI can sneak though. If AI output does become copyrightable, it will only be because of arguments that the controlling of that AI is sufficiently creative and deliberate to pass the minimum threshold required by law and the outcome isn't a random or uncontrolled result. Saying that it's "just like pressing buttons on a camera" does you no favors, if photography was just pressing a button then it wouldn't be copyrightable.
And in fact, there was an 1884 Supreme Court challenge over photography copyright that was predicated exactly on the argument that photography was a purely mechanical reconstruction of an existing scene (https://blogs.loc.gov/copyright/2020/09/historic-court-cases...). The argument was rejected not because purely mechanical reconstructions are copyrightable, but because the court disagreed and said that photography was both an act of human creativity and that it had a controlled outcome, similar to "writing" or "engraving".
And note that a critical component of "writing" or "engraving" is intent and control. When you write down something on a page, you get the result that you intended to put on the page; you control the "words" that appear. An important question when discussing AI copyright is what the threshold is where we can say that use is actually controlling the AI. A vague prompt might not qualify, an extremely specific prompt that is itself a creative expression might? A more guided process might? (although it's not certain if this would cover the resulting image or just the prompt itself). This is all untested in current law.