New Yorkers may exaggerate from time to time. But I have been at the 1st Avenue L stop during the morning rush and had to let 3 trains go by before getting on to the fourth (probably 20 minutes total waiting). I probably should have walked at some point but then I would have had to pay again at Union Square.
1st Ave L is probably one of the most crowded stops in the morning for rush hour in the city, probably competing closely with Lorimer and Bedford L stops.
In PM out of the city Union Square is similarly packed, and the train is nearly empty once you pass Lorimer
When I lived in Chicago, the State Street Subway at evening rush hour would have every car packed literally sardine tight. They could barely close the doors and there was barely room to breathe, forget about sitting down. I'm sure it was illegal but the conductors seemed to just pack people on until there wasn't room for one more.