I agree, this is a great use of I/me. It's not over the top, and it adds to the article. Using I/me is a lot better than saying "when he talked with Time for this interview" or "when the magazine requested to talk to DiCaprio."
This was probably the best graph:
Then, as always, he starts to worry. "O.K., it's pretentious that I'm watching this." And again he predicts how it will come out in the article. "Leo looks strangely uncomfortable as he sees himself," he says, mimicking what he fears I will write about him. "There's a certain detachment in him. He's squirmish when his scenes come on." It is kind of him to do my work for me.
The I/me is funny and it takes nothing away from the article, dawg.