I think government agents certainly are permitted the same: it's called "shadowing". I know, reasonable suspicion and all that, but within the confines of a parent-child relationship, it is the parent that holds all the power, including the ability to define what "reasonable suspicion" means, and to act on that definition alone.

So no, I still don't see the fundamental difference between a parent claiming "I reserve the blanket right to monitor my childrens movements" and a government claiming the same on its citizens.

(edit: not saying they're equal, there certainly are differences in scale and execution -- but the fundamental policy is still one of distrust and subversion)