My understanding has been just the reverse, that a digital camera
with auto-focus requires a circular polarizer due to the fact that
a linear polarizer has 'lines' running through it that the AF
system gets confused by.
No, there is no such thing as "lines" confusing the focus system.
Only DSLRs (and camera that use phase detection) need a circular
polarizer, a linear will work on every camera.
That's because a linear polarizer cuts the light oscillatig in one
direction (that's simplistic, but bear with me). So you can cut,
for instance, vertical "waves". If a surface emits more waves
oscillating in one direction, you will cut more light from that
surface (thus, reflections can be almost totally avoided).
A DSLR needs, however, both oscillation types (vertical and
horizontal) to work properly. So a circular polarizer is a linear
plus a device that splits half the light (say, the vertical one)
into vertical and horizontal. That way, you've cut the reflections,
and you still have both oscillation orientations.
That's all.
