IMS, technically, they can have different reeds with them so they can tune to a piano or an organ or somesuch, but indeed:
When doing a gig with an orchestra (me on the organ), the oboe player was well grumpy initially, and explained what a hard time she had with this.
Me, I don't really know what the problem is, but at a guess: they're not bringing 60 reeds to cater for a whole range of to-be-expected tuning standards.
Edit: had used the word "fleece" for "reed".