Ahhh, ok. I just figured out the problem (but not the solution).
According to Apple:
In general, avoid using complicated framesets that rely on the ability to scroll individual frames because there are no scroll bars on iOS.
On the desktop, frames in a frameset can be independently scrolled as shown on the left in Figure 1-1. On iOS, scrollable frames in a frameset are expanded to fit their content and then a frame is scaled down to fit its region as shown on the right in Figure 1-1. Scrollable full-width inline frames are expanded to fit their content, too. All other scrollable inline frames can be panned using the two-finger gesture. See “Two-Finger Events” for the events generated from the two-finger gesture.
Because there are no scroll bars on the inline frames, this is not an optimal user experience for viewing web content on iOS, so avoid using framesets. Instead use columns as described in “Use Columns and Blocks.”
This creates an interesting puzzle for any web gallery that's to work both in iOS and on the desktop. I suppose an ok fix would be to just have forward and back arrows for navigation, like most people have. If those existed, then it wouldn't matter so much that the thumbs were hard to use.
I still don't know how to implement those.