When is an analog input amplifier needed?
There are several reasons to put a amplifier between the input signal and a A/D:

To scale the voltage.  This apparently not necessary in this case, but I mention it here for completeness.  If the A/D input range is 0-3.3 V, then you have to amplify a small signal or attenuate a large one to use that range optimally.

To add a offset.  If a signal is centered around ground, for example, you can't simply multiply it by a constant to get it into the 0-3.3 V range.  A opamp circuit can add a offset while otherwise leaving the signal alone, or it can add a offset while also adding gain.

To present a lower impedance.  Actually this is a form of amplification.  Most microcontroller A/Ds want the input signal to have no more than 10 k&Omega; impedance.  Some fast ones even require down to a few 100 &Omega; to achieve full specs.  Many real world signals have much higher impedance than that.  A opamp buffer takes care of the high to low impedance conversion.

To clip the signal.  Microcontroller A/D inputs are often specified for very little voltage outside their operating range.  Even a little current thru the protection diodes can cause erratic microcontroller behavior, or result in erroneous A/D readings on other channels.  A rail to rail opamp running from the same supply as the microcontroller can't produce a signal outside the A/D range, but can be more tolerant to out of range signals on its input.  Those signals can be more easily clipped due to higher impedance being more tolerable at the input of the opamp than at the input of the A/D.  Also, opamps are generally a bit more forgiving of out of range input signals.

To isolate the raw signal from the A/D.  Most microcontroller A/Ds have a sample and hold front end.  This usually means charging a internal capacitor, which can put a significant load spike onto the signal.  If the signal is used anywhere else, these spikes as the sample and hold capacitor charges up can cause trouble.  By isolating the A/D input with a opamp, you keep the spikes from feeding back onto the raw signal, and probably also provide more drive to charge up the sample and hold more quickly.

To provide some filtering.  You'd like to eliminate all frequency content above half the sample rate.  Precise filtering is better done digitally after the conversion, but rough filtering before the conversion can be very useful.  It is also the only place filtering to avoid aliases can take place.  Once aliases are added by the sampling process, they become indistinguishable from the real signal in the frequency domain.