I suppose they are, but I'm not convinced that a place open to the public 18 to 20 hours a day should be above the first amendment, and never allow patrons to make photographs. In many places, they've become something akin to Main Street, no? And apparently this mall had the local police presence, and not the rent-a-cop variety, so they were able to enjoy the resources of their local tax base? So again, in a place where patrons can expect little privacy, why should the photographer be harassed for making pictures of seasonal shopping?
In a mall that doesn't have posted anywhere that photography is not allowed, anybody can take pictures of everybody he/she wants. In private properties like malls whose function is to invite foot traffic, photography can be allowed at the owner's discretion.
What bothers me is the fact that we as photographers have give in to the fact that even if the law protects us, our rights get infringed frequently in many different ways.
I am surprised that this photographer actually accommodated those two fathers by erasing the images. In the US The law clearly states that nobody can ask you to see or erase the pictures legally taken without a court order, I wonder if in the UK the law is different.
I was talking with an ex cop sometime ago and he told me that there is a law that allows prosecution to anyone that may cause disturbance to children. Even if a photographer doesn't do anything to disturb a child by taking pictures, there are still grounds for the police officer to stop the "offender" and do background checks and so on, like it happened to me.
It is a sad thing that children cannot be photographed as freely anymore as they have been the inspiration for many masterful images.
But this is not the worst damage caused by public opinion's and police enforcement disdain for photographers.
As photographers won't have the freedom to document our children, in the future there won't be sufficient documents to honestly portray todays society. It will be a sanitized view that won't allow photographers to show negative conditions either economical or social, or the magical world that children live in. Tragically, the instinct that moves photographers to take pictures of children is the same as the one of the parent trying to protect the child from the preying lenses. It will take a lot of protesting and finally a high profile case to set things straight again for photographers.
And yes, the problem is "fear', the most destructive one: adults' fear.