No, some of the funding for the data analysis comes from the total mission budget. Each instrument has a budget to partially fund researchers who work on the data.

Also, don't forget overhead: if a researcher has a $100,000 salary, the grant needs to have ~$200,000 total. Some of that goes to health insurance, some goes to the general university budget and some goes to general equipment funds and such.

As I said, there were ~1000 people working on Cassini/Huygens when it got to Saturn. Around 2/3rds of those were in the US, I believe.

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"For a successful technology, reality must take precedence over public relations, for nature cannot be fooled." -- Feynman, at the conclusion of his Challenger report