Born Free means having no desires and being conscious of the Soul and its purpose. It also means free from all preconceived ideas and notions with no specific bondage or attachment to any form or mode of life. Moksha is only one aspect of it which means freedom from Ignorance, someone who knows who one really is. But even those who have attained Moksha and are inwardly free may yet remain tied to certain ideas in the mind or to a certain country or religion of their birth.
Difficulties are always there upon earthly life. The Seers, Yogis, Avatars all have difficulties, both in the nature as well as outside and around them. If you see the life of Avatars and even God realised persons, especially the Avatar, you will see them having more difficulties than the average person. Their burden is much greater because they are bearing it for many and not just their own.
There are rare souls who can return after Moksha but once upon earth they have to face the challenges. However, being conscious within they go through the difficulties differently and more consciously. Born free or returning after Moksha is not synonymous with the Avatar which is a special Divine Manifestation for a specific earthly work.