That's really cool, flux, I didn't know iguanas could be house trained (granted, I have never done any research on it either). I've always wanted one, but the life span is quite a commitment. Maybe I'll rescue one some day
Mine was litter trained too. She also was trained to do her business outside before she could ride on my shoulder. She seemed to understand the odd word too.
Certain individuals can be surprisingly intelligent.
I had one from the time I was a teenager until I had my first child in my late 20s who was very "dog-like". He knew individuals, went on road trips with me, sitting in the back window of my hatchback, and would poop on the lawn when I pulled the car over and let him out to do his business. After I was married he even learned not to eat the houseplants and to stay off the couch.
The others I have had have not been as intelligent, but maybe I have never had the time again to put into one as I had when I was a teenager- he did everything with me, even slept in my bed when I was a kid.
Although others have not shown as much intelligence, they are pretty easy to potty train. Iguanas are creatures of habit. Nearly all only poop 1x per day (although an individual I own now is an exception and has to go 2x per day). If you take the iguana to a plastic tub with about a couple of inches of warm water in it at the same time every day, and do not let it out until it poops, within 2 or 3 weeks it will go from soaking for 20 minutes or so before pooping to figuring out what is going on and pooping almost immediately- within a minute or so tops. After the poop, the tub is emptied into the toilet, washed and left to dry. The iguana meanwhile I give a 5 minute warm shower and quick soaping and rinse. Whole thing takes only several minutes 1x per day and I have clean iguanas who shed well as a result. The interaction involved between owner and iguana and the predictable situation for the lizard which makes it easy for it to understand what is going on and what will happen next, make it a good way to strengthen the relationship between human and lizard.
The smart one when I was a kid would go into the bathroom and scratch on his tub when he had to go. I did not have to follow a schedule with him. Others if you do not follow the schedule you can expect an "accident". In the summer, he is the only iguana I have ever had that I would trust to open the sliding back door, let him out to do his business and get a little sun, and then he would wander back in when he was done. I would always watch him from the window, but he always returned into the house on his own. Others I have owned would have wandered off into the landscape, but not him. He really seemed to enjoy being part of the family- would follow my wife around for handouts if he saw her eating, would crawl across the room and onto my lap for petting when I sat down to watch tv.
They are really neat lizards, but they require a time investment especially for the first 3 years when they are growing. They really need an hour of hands on handling daily for those years to socialize properly.
People claim they have tame ones that go wild when they are in breeding- I don't believe they were socialized enough on a daily basis when young. The males I have raised have never been like this- you could pet and handle them easily even when they have actually been breeding with females who laid eggs, so I know it was really breeding season.
Without that time commitment when young, they can often be a problem when older. With the time spent, they can be one of the most amazing, intelligent, lizard pets.