Your question is actually not about method overriding. It is about what class is referred to within a class ... construction in a module body.
When you do
module Bar
class << Foo
p self
end
end
# => #<Class:Foo>
the << Foo points to the singleton class of the Foo in the main environment because class << Foo cannot define the singleton class directly of a class Foo that has not been defined in advance. So it looks up for Foo that is already defined, and such class is found in the main environment.
When you do
module Bar
class Foo
p self
end
end
# => Bar::Foo
a new class Bar::Foo is created; the Foo points to this Bar::Foo that is newly created, and it does not point to the Foo in the main environment. In order to point to it, you have to explicitly specify that with ::.
module Bar
class ::Foo
p self
end
end
# => Foo