I think there's a couple of things going on.
In the schools where I work and in my LA, they don't fine for a one-off one day absence where attendance is generally good (above 96%). Can't speak for other LAs.
If you ask the staff who deal with attendance (usually office staff) they'll tell you they'd rather have "illness" on a child's record than "holiday" (which would usually be marked as an unofficial absence).
However, the child's teacher will tell you not to lie, because the kids usually blab their mouths and then have to deal with knowing they've betrayed a parent or carrying a lie and either is horrible for the child.
These points have been made by PPs.
I've just got one other thing to say... We choose our children's schools based on loads of things, but a big one is usually the OFSTED report. Generally, most of us want our DC to go to a school where the report is positive.
Schools are graded on attendance.
So, it's a bit mean/low to chose a school based on a good OFSTED and then play a part in making their next inspection more challenging by doing things like taking them out of school for your convenience which will feed into their data on attendance.
There's a part of me that feels that you chose the school based on their OFSTED, so it's not very fair that for reasons that makes your life convenient you do things that makes their next inspection harder.
I don't expect to be agreed with on this point.