Theres some total lack of understanding of dog behaviour here..
A dogs growl is the same as your voice saying 'hey, no, back off gimme space'.
To suggest that because a dog has growled once at another dog it is therefore dangerous is like suggesting that if you've ever asked someone to back off and leave you alone YOU are also dangerous..
Growling is communication, thats all, it does not signify that an animal is a danger!
We do not know if the OP's dog nipped the other dog, we know that the other dog has a wound. He could have been bitten by something else, he could have caught himself on something, he COULD have behaved extremely rudely to the OP's dog and not heeded a polite warning to back away, causing the OP's dog to nip in self defence.
If you choose to let dogs off lead and out of sight to play, as the other dogs owner did, then accidents may occur.
Details have been exchanged, the OP intends to do the right thing, no ones done anything wrong here.
As for the dog being dangerously out of control - that is not clear.
If the OP's dog recalled swiftly, then they were not out of control.
If the OP's dog was simply playing with another dog, that was not 'dangerous'.
'Dangerously out of control' applies when the dogs behaviour is dangerous to people or livestock (and another dog is not livestock) AND you can demonstrate that the dog was out of control ie, not responding to recall cues.
Nipping another dog as a result of an altercation between two dogs is not 'out of control' nor is it an offence.