I am going to dare to add an alternate opinion here, which I will try to substantiate with some facts
I don't think having your bird understand a cue to poo is necessarily bad but it can be implemented poorly and cause problems.
First, birds do indeed hold it for hours so it is physically possible and done naturally.
A few examples:
- Hens on eggs (may only come out and poo 1-2 times per 24 hours, it will be HUGE and it will be STINKY)
- Males who are sleeping in a nest hole or nest box will hold it overnight
- All of my juvenile birds that I raise know that they get out of their cage first thing in the morning to fly. They all hold that overnight poo and let it loose when they get out.
- Since my birds are naturally cavity sleepers, I provide them with a box to sleep in year round, they all hold their poo overnight.
It is not that birds can not hold it. It is simply that flight is energy intensive and it makes sense to relieve themselves often so as not to carry the extra weight. As an avid bird watcher and photographer I can tell you that when you see a wild bird perched and he suddenly decides to poo, you better get your last look or and prepare for the in flight photo because that bird is about to fly. If you observe your parrots carefully you will see this same behavior (assuming they are flighted).
It is absolutely true that you can convince your bird to hold it too long, even to the point that they will not go in their cage. This can be from over enthusiastic potty training or from punishing them when they potty.
All that being said, if you do want to potty train the suggested method is to say the cue right as they are pottying where you want them too and then offer praise and attention, if they potty anywhere else then you simply ignore it. Once the association is made it is like a toddler, every so often you ask if they have to go (give the cue). If you cue at the intervals that are close to the interval your bird would normally potty you will likely have an arrangement you both can live with.
The key is to do things on a natural schedule, use very light reinforcement and offer no negative consequences when they naturally potty on their own.
I hope this give you a little more insight into how you can train in a way that does not interfere with the natural rhythm of your bird's system.
My own personal method embraces all of the above. With six birds I have two semi potty trained and I only cue them first thing in the morning to go on their cage paper rather than down the front of my door where they are heading when they get out.
So while I don't see a problem with it per se, I don't use it much myself currently.