You're correct that I made a dumb mistake. In a tournament we want to calculate our EV in dollars of expected payout, not in chips. Here's the math I should have done:
1) Ungar folds, he is left with about half the chips in play, so about 50% odds of winning the tournament, and EV of ~$50K.
2) Ungar calls and is right, winning $100k.
3) Ungar calls and is wrong. I forgot that he'd still have chips left and assumed that this scenario was worth $0. In fact he'll have ~20% of the chips in play left, which is worth $20K intuitively but can be confirmed here: https://www.icmpoker.com/icmcalculator/
So if Ungar calls he needs to be right X% such that
1) Ungar folds, he is left with about half the chips in play, so about 50% odds of winning the tournament, and EV of ~$50K.
2) Ungar calls and is right, winning $100k.
3) Ungar calls and is wrong. I forgot that he'd still have chips left and assumed that this scenario was worth $0. In fact he'll have ~20% of the chips in play left, which is worth $20K intuitively but can be confirmed here: https://www.icmpoker.com/icmcalculator/
So if Ungar calls he needs to be right X% such that
$50K = $100K * X% + $20K * (1-X%)
X ~= 38%