Awa,
The AIM applies generally, and as such covers operations of all types. Generally speaking, a controller will give greater credence to what a pilot is actually seeing on the approach. Note 2 in AIM 5-4-4 states that controllers will consider information received from automated stations for their own purposes, but will place greater credence on what the pilot reports when determining what weather is really out there.
Specifically, when the pilot receives the automated report directly, it will be more recent than what the controller has recorded from the long line (land line). Therefore, the pilot will get the very latest weather, which may have changed or altered from what the controller is showing.
However, as you know, a controller doesn't determine what the weather is, for the purposes of determining if the approach may be flown.
If the automated station is reporting weather below minimums, you may not shoot the approach, unless the report is received below minimums after passing the final approax fix inbound. See 121.567.
What this states is that if the pilot is unable to receive the weather (the "minute weather"), the controller will issue what has been received from the long ("land") line. The controller would prefer that the pilot get the very latest directly from the automated horses mouth, so to speak but will issue the last weather received from the long line if the pilot requests, or is unable to get the minute weather.
It does not justify disregarding the weather reports to go have a look; this is not at all what note 2 says. The last sentence states: "When receiving IFR services, the pilot/aircraft operator is responsible for determining if weather/visibility is adequate for the approach/landing."
This information is already known to the pilot, and is found in combination with the approach proceedure to be flown, the pilot's qualifications, and the OpSpecs. Note 2 authorizes nothing, as the AIM is not regulatory. However, were it regulatory, it states nothing more than the fact that the pilot is responsible for determining that weather is adequate, based on the regulations under which the pilot is flying. Under 121, the guidelines are clearcut, and note 2 grants no permissiveness in deviating from those guidelines.