T3 specifically was about years after Kyle was sent back, so of course it was 2032. John wasn't raiding the Time Displacement centre for the first time in 2032, he was smug walking around in the open thinking that he had won. This is what happens when you have sex with Claire Danes. Death. She has a death pussy. Although I suppose the actual person Claire Danes might not be as sexually poisonous as almost every character she has been paid an inordinate amount of money to play.
Judgement day moved to Never at the end of Terminator 2 when Senator John Connor is seen playing in the park with his daughter on Michael Jackson's birthday, so that makes 3 times. But that only happened in the directors cut. Also when was Judgement Day before time travelling took a dump, spraying future tech all over the past. The very first Judgement Day could have been as late as 2060 if man had to invent that technology without help of irresponsible temporal refugees, or again maybe their was no Judgement Day in the naked baseline timeline because man invented Time Travel for shits and giggles in 2029, and then after misplacing technology, Skynet was born which is how man really fumbled the planet.
Cameron was sent back before the movie Terminators and Kyle because they blew up the Time displacement complex, so that no one else could come back "IT'S JUST HIM AND ME!" Remember the Emperor's non operational Deathstar in Jedi that turned out to be fully operational? John Connor decided not to bend over for destiny and attacked early... But wouldn't that cock block his own conception? Unless he snuck in when Skynet wasn't looking so that in 2 years he could still send his mom and dad on a first date? But that would mean that Skynet was sitting on it's thumbs for 2 years not sticking it to the humans with time travel when it had a fully loaded weapon it wasn't using. Skynet must have been wet for the web of time because it was winning. Even as it was losing the war with man it was winning the time war. John/Kyle on the other hand should have had no interest in preserving the status quo that was universally violating them. Point is: John didn't send Kyle back in 2027, John sent Cameron back in 2027 who are not only different people, but different genders, and one of them is not even a person.