That is not true. She does not base her philosophy on the greatest happiness principle. The motivations in her philosophy are whatever the individual holds as an interest, regardless of what that interest is.
In Rand's own words: 3. Man — every man — is an end in himself, not the means to the ends of others. He must exist for his own sake, neither sacrificing himself to others nor sacrificing others to himself. The pursuit of his own rational self-interest and of his own happiness is the highest moral purpose of his life.
Now ... am I going to believe you, or my own lyin' eyes?
Back to what you said:
The motivations in her philosophy are whatever the individual holds as an interest, regardless of what that interest is.
So if I like to torture people, and take their stuff -- if that's my interest, you're saying Rand would support it? No, she wouldn't. She'd say that "my interest" is not a sufficient moral justification, because it acts against the interests of others.
Which of course contradicts Rand's claim that every man is an end in himself -- if this were really true, my interest in torturing you need not be affected by your reluctance to submit to it.
The problem is, following Rand's first two points (objective reality and "going by the evidence") leads me to conclude that there is no absolute injunction against torture, theft, murder, and so on -- the only constraint would be my self interest (Rand's point #3), and whether I thought I could get away with it.
And, of course, there's no particular reason to claim that "my interests" are the true measure of morality at all. The theory of evolution, which has a strong scientific backing, suggests that "the good of the species" might be a better choice. At the very least, this is a demonstrably valid alternative to Rand's "absolute" individualist morality. Logically speaking, the existence of a provable alternative means that Rand's findings are not absolute after all -- so much for her "objectivity."
The problem here is that objectivists expect us to accept their underlying assertions as true and absolute. For example, an objectivist favority is the non-initiation of force. I happen to agree with this -- but the sad fact is that one cannot objectively demonstrate that it is an absolute moral requirement. Indeed, the evidence suggests precisely the opposite.
Thus, if non-initiation of force is to be accepted as absolute, the basis for making the claim must come from a source other than application of reason -- from God, for example.
When you get right down to it, the problem is in the claims of absoluteness: they cannot be proved by this allegedly logical philosophy. And without such proof, the foundation of objectivism collapses.