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First of all, they are not getting $1.2B. The lump sum cash value is $551.7M. The usually reported jackpots are presented in terms of the value of a 30 year annuity.
Second, those winnings are before taxes. After taxes, depending on the state, the person will walk away with $280m-350m.
Now, sure, that is still an absurd amount, but still like 1/4th the stated jackpot.
That's more reasonable.
Also most lottery winners end up dead or bankrupt within a few years of winning.
The Google response seems to agree with you, but this Berkeley study says the opposite:
https://www.stat.berkeley.edu/~aldous/157/Papers/kaplan.pdf
(Fixed link.)
Dunno if it's bad for mobile or just a bad link but I got a 404.
I guess that's my point