While this FREE t-shirt from Epcot was in fact free, it came at a cost. On our trip with the church youth group in 2012, one of our students got sick on Mission: SPACE at Epcot. It was not pretty! When he exited the attraction, the cast members immediately took him to the side and gave him a free orange t-shirt to change into. He was given a Disney bag to hold his original shirt along with the free, plain, orange shirt. I assume he got an orange t-shirt because he was riding the orange side. Maybe if he had been on the green side the shirt would have been green?
If you are worried about getting sick on Mission:SPACE or any other attraction, this shows you that Disney will take care of you. We did opt to go back to our room for him to wash his face, brush his teeth and rest a bit, but he got to keep his orange Epcot shirt!