Yes, but Canonical is not part of Debian "group" and MATE (as a DE) is an "alone group" not being part of any group but MATE itself (fork of Gnome). That way, anyone can take different parts and ensemble a new OS or piece of software. So, in the end, Linux distributions are heterogeneous Software while Windows is an homogeneous software (this is false in software engineering but is a nice way to explain it).
So the software may be part of another software but a group doesn't mean it is part of it. This way it lets users and developers customize and change what they want. Look at this thread.