I think you're looking at this wrong. The kid is an example for why the budget gets tight, it could be anything (buying a house, deciding to pay off your credit card), you're correct the company has no obligation. Hence why you're asking, not informing that they'll pay you $20k more.

"If you were worth $100K and you negotiated for that, then that's what you make" was true at the time of the initial negotiation. This is a separate negotiation, with a source "hey, company X will pay me 20% more"

No, you don't deserve $20k more as you didn't ask for it, you might if you reopened negotiations.