Saliva and stomach acids cause the batteries to leak corrosive chemicals and burn the person/dog (whoever) on the inside. The little boy is home safe and sound but not unscathed. He has a burn in his esophagus and a small portion of his vocal cords is not working, causing his voice and cry to differ. He's a very lucky boy.
Choking on batteries is always a hazard for small children and animals but button or disk batteries are more dangerous. Please don't just assume "they'll pass it" !
Consider a First Aid Course so you'll know how to treat choking and seek medical help.
The following is a bit of info I found on line to share with you from Culture of Safety, http://www.cultureofsafety.com/childcare/button-batteries-swallow/
Be safe, don't let pets and small children chew or play unsupervised with remote controls, cell phones, watches etc.