No, what he said was this:
"I've never had a boss that required me to work on my days off, without pay to boot, and I'm not about to start now."
This does NOT indicate that "he didn't realize that sometimes people have to work weekends and late hours to fulfill their job responsibilities."
I have a job that requires me to work well beyond my normal workday hours. I stay at work late and, if necessary, I go in to work on Saturdays (building is alarmed and not available on Sundays). But I am compensated for all this by my SALARY. The salary is paid for me to do the job, regardless of what hours it might take for me to complete that job.
However, if my bosses required something beyond that, I too would expect to be compensated for it.
. . . And so would MLB players. You see, they get additional money paid on top of their salaries for making the post-season. Each players' salaries are paid according to "championship seasons," what we fans call the regular season. By making the post-season, players are further compensated on top of their salaries (for each their teams qualify for) getting WC money, division series money, LCS money, and WS money. And WHY are they getting the extra pay? Because it is work beyond what their contracts stipulate. Or, because it's actually a part of their CBA, it would be more accurate to say that it is work required of them beyond the "championship season" their salaries specifically cover.
As you must know, salaried employees have contracts, and they are compensated by salary for such work. But if salaried employees are asked to do something beyond what is in their contract, it is not unreasonable to assume -- in fact, it in most cases would be expected -- to be paid for work done beyond the scope of the contract.