She is requesting a work-time reduction, not necessarily a work-load reduction, (and in fact possibly an attendance time reduction rather than a work-time reduction) and the argument back in an ideal world ought to be able to explain why her request would mean a reduction in team performance, not just something vague like 'because it will' or 'well if someone works longer hours they get more work done' neither of which is true. It does depend on the job and on the situation, but it seems that reduction in hours has been possible for others - even without getting into whether they are paid full-time or not, this would suggest that their original argument about it being soleley about suitable cover to be invalid.
The last point about HR isn't always true, but mostly - some HR departments do indeed get involved directly in managment activities, but the most common model is that this part of the HR function is given to line managers/teams collectively.
It could be that your manager is making this decision without making it from a 'team' perspective, instead separating requests out and dealing with them asw individual, so I would advise making a team functioning appeal, including workload - not heavy, but just to emphasise that it is team performance and team goals that are important to maintain, within which is the management of individual needs.
In your discussion, (if you have one) try to get an agreement at the beginning of the meeting -eg. Can we decide that the overall goal is to keep the team functioning, to make sure all the work is getting done on time, and secondly that we agree that above all team cohesion must be maintained, as a result of our discussion.
You can then make appeals based on your need to manage your workload, as well as the relationships with others and you feel that at a time of need for you, after a period where you have been managing to be in full-time when others are not, that perhaps whilst you are in a more demanding period, you could lean on others for, say six months, without a reduction in workload (for example).
I think you have a strong case.