Essentially, the “otherwise available for work” clause was a mechanism in the past that prevented claimants who were on these essentially caregiving benefits from moving to sickness. If you think of regular benefits, you have to assert that you would otherwise be available for work if you weren't sick, and so benefits flow for sickness. The structure of the legislation in the past, before the Helping Families in Need Act, was that the “otherwise available for work” test would deny people the availability to switch to sickness, if they were on parental or compassionate care, or now on the new parents of critically ill children benefit.
The change that was brought to the act in 2012-13 followed the logic that caring for an ill family member, an ill child, or a newborn baby is essentially work and that you are otherwise available for work, and that is by providing care to a family member.
You can switch to sickness and then you can switch back afterwards to the benefits that are intended to support caring for a family member.