Correct...at least on most "normal" cruises.
The difference between over 12 and 3-12 is typically a small amount. I've seen it as low as $21 and as high as $200, but normally it is $100 or less.
Under 3 pays 1/2 of the CRUISE FARE portion of the ticket that 3-12 pay, but pays a full share of port fees. It's the same thing as the onboard booking discount--only the cruise fare portion of the ticket is discounted, the port taxes/government fees remain the same.
OK, this is a totally FAKE example. Say the first 2 adults are $1000 + $50 port taxes.....and third passenger 3-12 is $500
2 adults (or first 2 any age) pay $2100 ($1000 + $1000+ $50 + $50
2 adults + infant would pay $2100 + $250 + $50. $250 is 1/2 of 3rd person fee.
2 adults + 10 year old would pay $2100 + $500 + 50
2 adults + 13 year old would pay $2100 + $500 + $50 + over 13 upcharge of small amount.