Confused by the circuitry in the switch box for my basement lights (installing 1st smart switch)
I tried hooking up the smart switch grabbing a random white for neutral from that twistie, but the switch doesn't work. I'm kinda thinking that those twisted whites either are not neutral or that they're not all the same and one of the other white ones is the actual neutral.


That is exactly your problem.  Collectively the bundle is neutral.  You can't however "grab a random white for neutral" out of the bundle and just hook it up one on one.   

The reason is that one of those white wires is the neutral that goes back to the panel, the rest of the bundle is going to the lights plugs etc that these switches are controlling.   

To hook up your new switch you need to get all the whites together and capped with the same wire nut.