Honestly, I'd have left out of embarrassment.
I'm trying to put myself in the situation of the other owner. I'm imagining that it was the very first time I'd seen my dog react like that. I might think that something about the other dog is making my dog act uncharacteristicly. Yeah, I still would have left (even though I got there first) because I'd be unsure why she's acting this way. ESPECIALLY if I saw that you were coming (or wanting to come) in. It would scare me.
Of course, if this is normal behavior for my dog, I wouldn't have her there at the dog park.