If the child is 2 at the beginning of the trip he does not need a ticket, even if he turns 3 while he is there. If he is three at the beginning of the trip, he needs a ticket. To not buy him one is dishonest.
If he is three you are supposed to buy him a ticket. I did not buy the ticket when my child was three and no one asked. I also did not buy her one at Typhoon Lagoon and no Cm asked there either.
Disney's rules are if the child turns three during their stay they do not need a ticket and if they turn ten during their stay they can use a child ticket for the entire stay. If they have their 3rd or 10th b-day before the start of their stay, then they need to buy the appropriate pass.
If you check in on the day your child turns 3 for instance, you don't need tickets the entire trip? And how is that verified, as far as when your vacation started?
It's really pretty straightforward. If your child is three at the start of the trip he/she needs a ticket for the whole trip. So if he/she turns three the day your trip starts, yes he/she needs a ticket. If he or she is 2 at the start of your trip, then he/she does not need a ticket, even if his/her birthday is the 2nd day of your vacation.
If questioned about age and your child turned three on the trip, you would simply tell the CM that your child's birthday happened while on vacation (I am sure your child would offer this up on his/her own).
You are asked for the ages of your children at the time the trip will be taken when you make your ressie. No one is going to ask you for a birth certificate when you check in. It comes down to the honor system and what morals/values you would like to teach your child (though people have certainly been questioned when trying to get an over-age child into a park).
So if you check in on a kid's birthday, then YES they need a ticket, but if its day 2 or your trip or later, then NO they don't. That doesn't make a bit of sense to me, but oh well...That's not straightforward to me at all...actually, it really doesn't make much sense. Not to mention I can't seem to find anywhere that Disney states that this is the policy.So if you check in on a kid's birthday, then YES they need a ticket, but if its day 2 or your trip or later, then NO they don't. That doesn't make a bit of sense to me, but oh well...
I think that if Disney was gung-ho on making every 3 year old pay, they would either ask for proof of age (like on flights) or make the cut off by height so they could determine who pays and who doesn't rather than the honesty policy they have now.

I can't find on the Disney website where they talk this policy. Anyone have a link?

Here is our experience. Our son will be three in October. He is 40 inches tall, and people always believe he is older than he really is. We go often to Disney, with the latest trip in June. I carry his birth certificate in case someone should ask. We have never been asked by a CM how old he was, nor has he even been asked. So, they really do seem to "trust" you to do the right thing here. In fact, the only odd looks I have ever gotten were from people who see me changing him in the bathrooms. I feel like shouting that he is really only two.