Which One of You Guys Is Leading This Project?

Last week an interesting, sad and funny conversation took place between my colleagues and me.

I have a colleague that came to my company a few months ago. She is working on the same project as I am from the first day she came to the company. (Occasionally she works on some small tasks on antoher project .)
And so, during the break, a few of us went for a cup of coffee to the nearby cafe. We were again (unfortunately) discussing everyday company issues/problems. In the middle of the conversation about the project we are working on (I can't even remember what this conversation was about) this colleague told me:

"You should decide about that." (... whatever it was ;) )
I said: "Why?"
She: "Why? Because you are leading this project."
Me: No, I don't.
She: "Then who is?"
Me: "XYZ is."
She: "OK, him too. But you lead it also. You are doing it together."
Me: "No we don't. It's just him. He is the project manager and the team leader. Officially and unofficially."
She: "OK then, I didn’t know that..."

I will not comment this because it happened to me and not somebody else and it will look like I’m bragging. But there is something seriously wrong with this picture. And even though it's funny, it's not difficult to guess what the status of the project is.