Challenging project story with Uber during a job interview at another SV giant

I'm currently interviewing for project manager roles and I am expecting a question about a challenging communication or collaboration in my past experience.
There was one with Uber when while working in tandem with a few of their teams, their PR employee in San Francisco did not want to cooperate and help fulfill the project. Eventually I found a new contact in Washington that turned out to be helpful and we ended the project successfully.
In the interview, I'd most likely be more specific what the project involved since that accounts to my experience.

Do you think that this is too sensitive information to share during an interview at another big giant in Silicon Valley? Would I come across as sharing some gossip, etc?

It's a good example for me because it was a clear success but the larger the brand the more hesitant I am to share any examples.