This is probably the reason why they didn't make an exception. It's not the fault of any kid that they get ill, so if they made an exception, they'd then have to allow every kid who had a genuine illness and reason for not being at school one day to come. But the problem is: how do you then...
Speaking from the experience of my missis being a primary head, your first paragraph is spot on.
Rules such as not allowing kids the odd day or two off in term time aren't there to punish Mr and Mrs Nice who support their kids' education but have valid reason to take their kids out of school...