It's basically understood that unlimited PTO means untracked and within some reasonable amount - if you were at an At Will company in the US they don't owe you much. Obviously you can't just take 3 years off of 'unlimited PTO' so it's hard to claim you truly believe it's limitless imo.
Expecting a promo when you're not working and expecting to be able to just take infinite vacation (even when dealing with tragedy) is just not realistic. There are other options (medical leave, extended leave, etc.) - some companies will go out of their way to be kind, but I wouldn't have that as my expectation.
This kind of rant doesn't look great either - my take away is this person was probably just difficult in general, there may have been other reasons they were not promoted.