When we took the tour last year, we were told by the Dis'er who booked the tour for us that we needed to produce IDs for only the adults in our party. On the day of the tour, my husband and I had our driver's licenses with us and showed them to the Disney CM who in turn proceeded to cross our names off the official tour list. Our daughter did not have to produce an ID.
My guess is that Disney requires IDs so that only the people who have booked the tour can take it.
I read a couple of weeks ago about an unofficial tour at another theme park where some unexpected guests somehow became part of the wrong tour. Had they been asked to produce IDs when they joined up with the tour, the mix-up could have been averted and the guests could have gone on the tour that they had booked instead of the unofficial tour that they had accidentally became a part of.