In reality, if you want to get the benefits of a factory class, you need the static method in it's own class. This will allow you to later create new factory classes, or reconfigure the existing one to get different behaviors. For example, one factory class might create Unicorns which implement the IFourHoovedAnimal interface. You might have an algorithm written that does things with IFourHoovedAnimal's and needs to instantiate them. Later you can create a new factory class that instead instantiates Pegasus's which also implement IFourHoovedAnimal's. The old algorithm can now be reused for Pegasus's just by using the new factory! To make this work both the PegasusFactory and the UnicornFactory must inherit from some common base class(usually an abstract class).
So you see by placing the static method in it's own factory class, you can swap out factory classes with newer ones to reuse old algorithms. This also works for improving testability, because now unit tests can be fed a factory that creates mock objects.
I have done the latter before (static factory method on the class that you are creating instances of) for very small projects, but it was only because I needed it to help refactor some old code, but keep changes to a minimum. Basically in that case I had factored out a chunk of code that created a bunch of ASP.NET controls, and stuff all those controls into a user control. I wanted to make my new user control property based, but it was easier for the old legacy code to create the user control with a parameter based constructor.
So I created a static factory method that took all the parameters, and then instanced the user control and set it's properties based on the parameters. The old legacy code used this static method to create the user control, and future code would use the "prettier" properties instead.