As a Falsehood
Humans are often known to voluntarily: donate their time to a charitable cause for the poor, convert to a vegetarian diet for animals, and sacrifice themselves for their comrades in a war situation such as when one covers a grenade with their body. These acts do not reward the actor*, thus invalidating the premise that the idea is universally applicable, and rendering the idea false.
As a Tautology
A tautology is a logical statement that is all-encompassing, and thereby true but devoid of value. An example is, “All things are either A or not A.” If psychological egoism reasons that an action to help another is motivated an underlying (selfish) “good feeling” reward, then all actions are either overtly selfish, or covertly selfish in the case of overt selflessness. If this is true, the idea is recursively descriptive of human behavior and therefore devoid of value. Logically,

The logical statement a = a, the result of the reasoning, lacks any insight whatsoever. Moreover, it is only notable that bananas are yellow because it is logically possible for bananas to not be yellow. If yellow were the only color in the spectrum, this (albeit logical) observation would be meaningless. If the ideas of a yellow banana and a banana are always interchangeable, there is no value in labeling the color of the banana. Similarly, if motivation is always selfish, there is no value in labeling the nature of the motivation.
Conclusion
The flaws inherent in the idea of psychological egoism can also be ascribed to its inverse, psychological altruism. The underlying error common to both – the oversimplification of human motivation – implies the presence of either a pluralist or transcendental truth.
* Save a possible psychological reward which is inherent in the definition of any psychological motivation and therefore not a distinguishing characteristic of any type of motivation in particular (refer to “As a Tautology”).