Human bites are nasty. The human mouth is full of lots of bacteria. I'm an doctor and we routinely give the strongest oral antibiotics (sometimes even IV) for human bites that pierce the skin and draw blood (which this one did), even if it's just a piddly one from a toddler.
Where the hound was bit was pretty nasty too. On an arm or a leg the infection could be more localised, but the neck, it's going to spread.