Welcome to the Asana Community Forum @Karen_Knight 
That means she has clicked on the message so she could read through the task in detail or she only scrolled over the message in the inbox? If she only scrolled over the message in the inbox without actually clicking on it it won’t mark it as read.
I have just tested this and it works on my end to mark as unread and when I open the message it gets marked as read automatically.
I would ask her to test in incognito mode also and clear the cookies, maybe that helps. Otherwise ask her to reach out to Asana support so they can look into this. Best will be including a video showing the problem.
I definitely agree this is best practice. Whatever has been attended to and does not need further action archive. Whatever needs further action add a subtask or follow-up task directly.
In my opinion the goal should be to always keep the inbox clean and empty.
Here is a great post about it as well.