EDIT: Well I'll be damned, the output does track the input for voltages less than the set point...
Why wouldn't it?
A linear regulator is going to
try to keep raising the output voltage if it thinks it is low, it just won't be able to actually
do it if the input voltage falls much below what it is trying to output. Older, simpler regulators "drop out" of regulation and just run "full-on" with perhaps a volt or two input-output differential. Newer LDO (Low Drop Out) voltage regulators will still stay in regulation to a
lower differential (often only 100-300 mV or so of drop, as pointed out in posts above) which may be negligible (enough) in some applications. YMMV, depending on your application, of course...
In order to actually output a voltage higher than your input, you would need to move to some sort of switching converter that includes boost mode operation.