A really interesting situation took place last night and I couldn't find any information on how this should be ruled anywhere.

Five people left in small MTT, significant pay jump between fifth and fourth.

BB starts the hand with 80,500 chips, pays the BB ante of 3,000. So now has an effective double up stack of 77,500 chips.
UTG starts the hand with 79,000 chips.
Button starts the hand with 100k+ chips.

UTG, Button, and BB end up all in and button scoops the hand, and both BB and UTG are eliminated.

The question is, should BB get 4th place because they started the hand with more chips before the BB ante was paid, or should UTG get 4th place because the BB ante is dead money that "can be won by anyone" and they did indeed stand to still be in the tournament with 3k chips if BB scooped the pot but they won the side pot with the button?

When you put the blinds and antes, the chips are no longer yours. They belong to the pot

The shortest stack will have to take 4th here, and is the player in the BB

But do you base shortest stack off stacks before or after blinds and antes are put in?

considering players technically don't get their cards until they have paid the ante and blinds. so basically you have to pay for your cards. BB had to pay a little extra. the math is fine.