I quote you, (again), "she rejected the collective (the concept that the group is more important than the individual)".
You are wrong because Rand did not consider the group to have any importance at all. There is no question in Objectivism of which is more importat, the individual or the group. With regard to the concept importance, a group is irrelevant, unless an individual has some personal goal or objective with regard to a group (is forming a football team, for example), and then the importance of the group is derived entirely from the intentions and purposes of the individual.
Hank