Here is my take in this and as a non coffee drinker I don't have a dog in th fight.
My belief is what it comes down to are a few criteria, supply, taste and exposure. Whoever was going to supply those had to be able to meet the supply Disney needs. I am sure there are many fine coffees out there but if they can't give all that Disney needs it doesn't make sense to use them.
Second, the company sponsoring has to be somewhat of a name. With that they have to have the money to sponsor it.
These leave only a few suppliers around to handle it. Starbucks made a logical choice.
While I was unaware a Stsrbucks guy was on the board, this could be a non issue as the supplier still has to meet the above criteria. No think it made it A LOT easier to get Starbucks in the parks because of that though.