That's technically wrong, the worst kind of wrong. If you rent a house, the backyard is owned by your landlord. Sure in casual conversation you will say "my backyard", but we're talking about ownership here.
And we're talking about how a (loose) organisation is branded, not the legal implications. The "backyard" in question is already one metaphor deep, for crying out loud.
This is like complaining that Amazon has little to do with the rainforest.
This is like complaining that Amazon has little to do with the rainforest.