I agree with this, but for different reasons. The difference between "Edit my profile" and "Edit your profile" is really a difference in how the relationship between user, interface and back-end system is conceived. When the interface says "Edit my profile", it's represented as speaking for the user to the system, so you have [user+interface] <---> [system]. Which is a technically accurate representation of client-server architecture, and also generally the way the world looks from the perspective of any system - the UI is decoupled, and speaks to the system on my behalf, in my voice. This is the system-centered perspective.
To the average user, the world looks quite different: [user] <---> [interface+system]. Here, the interface isn't part of "me", it's outside, part of the system, so it should speak as the system, not as "me". This is the user-centered perspective, because it reflects how users see the world.
I think this also speaks to why programmers generally tend to be bad at user experience - it's almost an ontological problem. What is software, really? Is it just system, with interface added in later, almost as an afterthought? Or is it interface+system?