If you know the owner of this other dog and you know he's all up to date on shots and stuff, I think it'd be ok. I wouldn't take Charlie to a dog park yet or let him play with dogs you don't know yet.
Seconding this. What is the most important thing is your puppy's health, and even if you have to compromise what he can and can't do in the mean time, it's nothing compared to what could happen if he caught something he hasn't been inoculated against.
Temporary set-back for a lifetime of happy doggy moments!
If you know for sure that the other pup had all his shots, then it's probably ok to let them play together. It's important to protect your pup til he's fully vaccinated, but equally important to make sure he gets lots of new experiences while he's still within the socialization window that closes at 14 to 16 weeks. Having good experiences with friendly, vaccinated dogs is an important part of socialization if you want your pup to interact with other dogs when he grows up.
It's ok to let them play. I'd just check and make sure the other dog is vaccinated. My vet let me start taking Seanna to the dog park at 4 months. It's good to let him get socialized as much as you can.