A LDO on four 1.2 Volt batteries won't work, 4x1.2 is 4.8 Volt, and LDO's need at least more than what they output. Often something like half a volt more, so they need 5.5 Volt to output 5.0 Volt.
% batteries would give you 5x1.2 Volt = 6.0 Volt, which would work fine, even if the battery outputs dropped a bit to say 1.1 Volt.
Feeding the PI directly on 4.8 volt (four batteries) might work for some time, but is not ideal, as the moment the batteries are not completely full it will stop working. Also the maximum the PI may be fed with is just 5.25 Volt, and a protection device (tranzorb) D17 would short circuit any higher voltage to ground, leading to excessive currents flowing if you try to put more into it.
The earlier stories about the PI working directly on batteries was about the beta version, which had a 6.0 to 7.5V DC input, with a 5V LDO pre-regulator directly after the power input. This idea was dropped for having a mini USB port without any pre-regulation for 5V. This beta version would have worked with four 1.5 Volt (not 1.2 Volt) regular batteries, as they would have provided the required minimum of 6 Volts.