I don't want to defend ALW, but, for what it's worth, the use of 'my' is common in the theatre community. Look at Tony Awards speeches - performers will often thank "my director", "my cast". It's a phrase not unique to ALW
I invite you to listen to awards acceptance speeches (in film and television as well). References to "my cast and crew" are very common. It's something that's always rankled with me. Like you, I've always used 'our'.
