It's a pain sometimes (some big shopping centres have some nice displays during certain times of the year!) but yeah, as it's private property they can ask you to stop taking photos or be escorted out. They can even, if they really wanted to (though it'd be bad for business) kick you out because they don't like your face.
Doesn't mean taking photos is illegal as such, just that if they don't allow it they have the right to boot you out.
Malls being private property and not some sort of public rights-exercising ground is a concept that some have still to learn (WHY ARE YOU CLOSED? I HAVE A RIGHT TO SHOP!) :)
Reasoning for being told not to take photos seems to vary, but when I was asked to put my camera away once - politely - the reason given was "the shops get a bit upset about their copyrighted logos", which is probably where the claims of illegality come in. And knowing how extremely touchy companies tend to be about their logos, it's not entirely surprising if it's the most popular reason that brought forth all this fuss to begin with.
It gets a little different, I believe, if you're taking pictures of the mall (including any outward facing shop windows) from the outside, as there you would be in a public area and they have chosen to display things in view of a public area. I've heard of photographers being asked to leave from in front of a shop on a public high street and, basically, being able to say no. Though I suspect depending on the side the policeman's on if they got involved, they could possibly think up some sort of public order offence.