What was the other dog's body language like before your dog got there? Body position, tail position etc. What was your dog's greeting like? Did he rush right up to the other dog's face and THEN stop? Rushing at a dog you don't know can be seen by some dogs as rude and confrontational. A butt sniff and then a face sniff (no proctology exams) is a good greeting.
If the other dog turned his head away when he was being sniffed I would have called my dog then. He's saying that's enough. If it escalated to the stiffen and growl it probably was too late to call him (which you found out) as the movement triggered the other dog to react in chase and bite as opposed to just a corrective snap and get out of my face.
Are the dogs "equal match" in body size? Is your boy neutered? (as this can trigger aggression in other males..not always, but sometimes)
A lot depends on your dog and his dog skills. What I mean by dog skills is does he have the communication skills necessary to know when to turn away if a dog is giving him the "you're in my space" signals? If he DOES I would watch carefully but NOT call him, while walking over to get closer in case things escalate.
I walk dogs professionally and each one has different levels of skills, one of my goldens has terrible greeting skills so I call him BEFORE he gets to the other dog as I know he tends to rush the greeting, gets told off and then reacts. Once I have him we walk over and have controlled greetings and we're good to go.
I know Cracker ONLY tries to rush dogs that are insecure (bullying) so I don't allow her (thank god for good recall) to rush dogs either. If everyone is calm they get to say hi, play or whatever. If there is an exchange that is slightly tense but I can see from body language that it is CONTROLLED intensity I watch carefully but let it unfold. Some of my other dogs NEVER have issues as they approach calmly, give a "how do you do sniff" and then either play bow or walk away to greet someone else. That is the ideal..lol.
There are many more subtle signals going on in a ten second greeting than we think. Some LOOK bad to us and arent', some look fine to us and are actually precursors to aggression. Knowing YOUR dog and having a pretty good background in dog communication and body language can help prevent things from happening in the first place. Eight years and only three biting incidents (none serious)..by being watchful and knowing the dogs.