The finger thing you're referring to doesn't take fingerprints. It is doing a quick scan of the bones in your finger(s), and coming up with a mathematical figure, representing the relationship between the lengths of some of the bones in your finger(s). The Disney computer database will then "assign" your park pass that number the first time you use the pass. Each subsequent time you enter a park, you will again have to use the finger scan device to prove your pass is yours and not someone else's. If you gave or sold your multi-day pass to someone else, that person would not be permitted to enter the park, because their finger scan number would not match yours. The CM in the area will be alerted to this by the turnstile/computer, and the person would then be asked to show ID; when their ID doesn't match the name on the pass, admission will be rejected.
It's against Florida law to sell partially-used multi-day theme park passes, and it's against Disney's contract with you (when you buy it) to give it away. In other words, multi-day park passes are non-transferable, and the finger scan is Disney's method of trying to enforce this.
Finger scans like the one Disney uses aren't foolproof eben when they work perfectly, because unlike fingerprinting (there are no 2 alike), finger scanning is good for about 1 in 1,000. The odds of someone selling their partially-used multi-day pass to someone with the same finger scan reading would be about 1 in 1,000, which is close enough for that purpose.
SO, never fear, Disney will not have your finger prints!
Kids 9 and under don't need to use the finger scan device at all.
Reportedly, all passes on the same reservation are linked. As a result, a husband and wife could accidentally switch passes and use each other's, and there will be no problem gaining admission.