Von, sounds like they were grasping at straws and they dont' actually have a documented policy on it?? That reasoning is dumb!
I think the signs should say 'parents with small children'. That's how i interpret them anyway.
I, too, took it as a symbol for parents with kids in tow. Actually, when I have thought about it, I thought it made more sense to reserve these spots for parents WITHOUT prams, because then their kids aren't restrained and are safer closer to the centre! Also, if you're using a sling, just that little less hiking to find your car when you're carrying your child AND the shopping is far more convenient.
Quite frankly, I use the spots less (or look for them less) when I DO have the pram, because it means DS is restrained and I'm not carrying his weight on my dodgy hips...and walking further to the car is far less problematic!!
I love parking people in - we do it from time to time at the fire station where tourists can't seem to understand "No standing at any time, CFA vehicles excepted"...yeah, it's a bit vague, isn't it?? As vague as a spot with a pink line around it and the pink diagram of a parent and a pram...