GREAT news

That's wonderful
Sometimes it SEEMS aggressive-but dogs are predators-so their 'play' is acting out hunting and predator behaviors.
Go with your gut-BUT I would say-if there wasn't blood and it seemed out of hand-it wasn't.
We go often to the dog park (about 5 times a week minium) and less then two days a month go by without Mikey playing with dogs-either at the dog park or at home or at friend's houses. He is super well socialized imo and a very safe, dog friendly dog.
When you see him playing it can look and sound awful-they are growling, excited, baring teeth, rolling, biting legs, biting ears, biting necks, biting collars, chasing and jumping -and in general look nuts. I admit-the first few trips or times he played with others-I was alarmed at it!
But they are just playing.
And in short-if you didn't get bit prying a dog off your dog, or didn't need to pry a dog off your dog-then they were not fighting.
Crio has an excellent idea on this-pull the two dogs apart-and let the dog go who seemed to be the underdog-the one you thought was being attacked. If he runs right back to the other-the one you thought was aggressive-they are just playing
I want to disclaimer this with 'use your gut instinct' because you don't want to 'turn off' if they are fighting or there is danger-but I really doubt that
In short-to answer your question-yes I think she would be different if you brought her by herself-as she might be more timid or something to that effect. I'm sure she was more confident with buddy at her side.
Also it's important to have room to escape-is the dog park large enough that a dog can leave-run away a bit if they are being bothered? It's when dogs are leashed or trapped that they can fight.
Another way to tell is if they do any 'play bows' -thats a definite sign of play