I doubt it is that simple, especially as noted the sheriff said the child ran from him, that triggers two things, whether it was exigent circumstance (child was in danger, he ran after them) or that the actual running gave probable cause to believe they were an elusive suspect. Both things have been upheld, but they would probably go with the first because its a child, and well “won’t somebody please think of the children!.” This may be alot of things but an easy dismissal it would not be.
I am not saying you are wrong, just legally the cop could make the argument for Exigent circumstances and easily win.