In the US corporate world how often are people "sick with the flu" versus forced to work overtime?

In my experience it's fairly common to not have to work much overtime even on a salary. It's just a few certain types of industries and certain types of positions where this is heavily abused.

I worked in the gaming industry in canada for a brief stint and there was a period where we had mandatory team overtime of 4-5 hours M/W/F for a few weeks.

The only saving grace of going through that was that team productivity tanked so badly that the company ended up losing progress toward the milestone and payed out of that contract. After that experience dev estimates carried more weight and the company was more cautious about tight deadlines.