The feat specifically states it at the end of the description in the PHB (emphasis mine):
you do not gain the ability to speak while in a wild shape.
Furthermore, the feat clearly states that the verbal and somatic components are replaced by sounds and movements that the animal can normally make, such as the stated example of a hawk in the PHB:
For example, while in the form of a hawk, you could substitute
screeches and gestures with your talons for the normal verbal and
somatic components of a spell.
However, the question regarding the material components is a very interesting one as that is not explicitly stated in the feat text. The PHB text is as follows:
You can also use any material components or focuses you possess, even
if such items are melded within your current form.
To interpret the word use here we have to look at page 174 of the PHB which states what use means for both a material component and a focus (emphasis mine):
Material (M): A material component is one or more physical substances
or objects that are annihilated by the spell energies in the casting
process. Unless a cost is given for a material component, the cost is
negligible. Don’t bother to keep track of material components with
negligible cost. Assume you have all you need as long as you have your
spell component pouch.
The description clearly states that any material components are destroyed. Now let's look at the description regarding a focus (emphasis mine):
Focus (F): A focus component is a prop of some sort. Unlike a material
component, a focus is not consumed when the spell is cast and can be
reused. As with material components, the cost for a focus is
negligible unless a price is given. Assume that focus components of
negligible cost are in your spell component pouch.
Here the description clearly states the when using a focus, it is not consumed. Therefore, combining the above it is clear that the feat allows the caster to consume the material components that the original form had on him, as well as allowing the (re)-usage of a focus. This also maintains balance as giving them "the abilities required to fulfil the spell's requirements" would lead to balance issues with spells that use an expensive component (to prevent over use).
Summary
- Natural spell does not allow one to speak.
- Natural spell allows one to substitute verbal and somatic components with animal sounds & movements.
- Natural spell allows one to consume components that are carried in the original form.
- Natural spells allows one to (re)-use a spell focus.