This was useful when there was a BLOCK_UI mode where f() was called
differently, but now we no longer need it. I'm making this change as a
separate commit because folding it into the previous one (which would
conceptually have made sense) would have made that diff unreadable
because of the indentation change.
The variable `fRunsOnUIThread` and its comment no longer make sense now;
we'll clean this up next.
The diff is best viewed with --ignore-all-space.
d70d70aad2