simple low noise regulated supply

[rayma]

"It is not necessary to bypass the out- put, although this does improve transient response.
Input by-passing is needed only if the regulator is located far from the filter capacitor of the power supply"

These are heavily internally compensated, with the resulting poor transient response.
Look at the output impedance rising above 1kHz, for example.
A power supply should be much better in these respects than the circuit that it powers.
A good Linear Tech note on testing by the late Jim Williams, check out Fig. 12:
http://cds.linear.com/docs/en/application-note/an104f.pdf