With regards to attempting to 'use' a ticket he'd paid for to give his toddler a seat, I went through something like this last year. 

My wife had a return ticket. It turned out she could not leave at the scheduled time. Okay, I thought, I'd just buy her a one-way ticket to where we were going and use the return portion of the ticket. 

When I talked to the airline people, however, since my wife wasn't on the outbound portion of the ticket, they automatically cancel the return portion. The solution was to change the departure of the existing return ticket which didn't cost much more to do than purchasing a one-way ticket. 

Seems crazy, but YOU can't just buy a block of tickets and then decide who among your group uses them. The tickets are sold to specific people and they have to use them.

If they don't check for ID, possibly the man could have claimed the toddler was the person the ticket was issued to??

And yes, Welcome to 'Airline Land' where up is down and left is right.